Sequences

392,541 sequences

Least k>1 such that reverse complement of first n terms of A006928 repeats beginning at k-th term.A025511
Least k>1 such that reverse complement of first n terms of A006928 repeats beginning at k-th term.
Index of n-th 2 in A022300.A025512
Index of n-th 2 in A022300.
Exactly half of first a(n) terms of A022300 are 1's (not known to be infinite).A025513
Exactly half of first a(n) terms of A022300 are 1's (not known to be infinite).
Sequence A025513 divided by 2.A025514
Sequence A025513 divided by 2.
Least k such that first k terms of A022300 contain n more 2's than 1's.A025515
Least k such that first k terms of A022300 contain n more 2's than 1's.
Index of n-th 2 in A022303.A025516
Index of n-th 2 in A022303.
Least k such that first k terms of A022303 contain n more 1's than 2's.A025517
Least k such that first k terms of A022303 contain n more 1's than 2's.
Least k such that first k terms of A022303 contain n more 2's than 1's.A025518
Least k such that first k terms of A022303 contain n more 2's than 1's.
Least k>1 such that first n terms of A022303 repeat beginning at k-th term.A025519
Least k>1 such that first n terms of A022303 repeat beginning at k-th term.
Least k>1 such that reverse of first n terms of A022303 repeats beginning at k-th term.A025520
Least k>1 such that reverse of first n terms of A022303 repeats beginning at k-th term.
Least k>1 such that complement of first n terms of A022303 repeats beginning at k-th term.A025521
Least k>1 such that complement of first n terms of A022303 repeats beginning at k-th term.
Least k>1 such that reverse complement of first n terms of A022303 repeats beginning at k-th term.A025522
Least k>1 such that reverse complement of first n terms of A022303 repeats beginning at k-th term.
a(n) = 1 + Sum_{ k < n and k | n} a(k).A025523
a(n) = 1 + Sum_{ k < n and k | n} a(k).
Number of positive integers that are not the sum of distinct n-th-order polygonal numbers.A025524
Number of positive integers that are not the sum of distinct n-th-order polygonal numbers.
Largest number that is not the sum of distinct numbers of form k^2 + n.A025525
Largest number that is not the sum of distinct numbers of form k^2 + n.
Number of positive integers that are not the sum of distinct numbers of form k^2 + n.A025526
Number of positive integers that are not the sum of distinct numbers of form k^2 + n.
a(n) = n!/lcm{1,2,...,n} = (n-1)!/lcm{C(n-1,0), C(n-1,1), ..., C(n-1,n-1)}.A025527
a(n) = n!/lcm{1,2,...,n} = (n-1)!/lcm{C(n-1,0), C(n-1,1), ..., C(n-1,n-1)}.
Number of prime powers <= n with exponents > 0 (A246655).A025528
Number of prime powers <= n with exponents > 0 (A246655).
a(n) = (1/1 + 1/2 + ... + 1/n)*lcm{1,2,...,n}.A025529
a(n) = (1/1 + 1/2 + ... + 1/n)*lcm{1,2,...,n}.
a(n) = (1/1 - 1/2 + ... + (-1)^(n-1)/n)*lcm{1..n}.A025530
a(n) = (1/1 - 1/2 + ... + (-1)^(n-1)/n)*lcm{1..n}.
a(n) = (2nd elementary symmetric function of {1/1, 1/2, ..., 1/n})*(lcm(S))^2, where S = {1,2,...,n}.A025531
a(n) = (2nd elementary symmetric function of {1/1, 1/2, ..., 1/n})*(lcm(S))^2, where S = {1,2,...,n}.
a(n) is the sum of exponents in the prime factorization of lcm{C(n,0), C(n,1), ..., C(n,n)}.A025532
a(n) is the sum of exponents in the prime factorization of lcm{C(n,0), C(n,1), ..., C(n,n)}.
a(n) = (1/C(n,0) + 1/C(n,1) + ... + 1/C(n,n))*L, where L = LCM{C(n,0), C(n,1),..., C(n,n)}.A025533
a(n) = (1/C(n,0) + 1/C(n,1) + ... + 1/C(n,n))*L, where L = LCM{C(n,0), C(n,1),..., C(n,n)}.
a(n) = (1/C(n,0) + 1/C(n,1) + ... + 1/C(n,k))*L, where k = [ n/2 ], L = LCM{C(n,0), C(n,1),..., C(n,n)}.A025534
a(n) = (1/C(n,0) + 1/C(n,1) + ... + 1/C(n,k))*L, where k = [ n/2 ], L = LCM{C(n,0), C(n,1),..., C(n,n)}.
a(n) = (1/C(2n,0) - 1/C(2n,1) + ... + d/C(2n,2n))*L, where d = (-1)^2n, L = LCM{C(2n,0), C(2n,1),..., C(2n,2n)}.A025535
a(n) = (1/C(2n,0) - 1/C(2n,1) + ... + d/C(2n,2n))*L, where d = (-1)^2n, L = LCM{C(2n,0), C(2n,1),..., C(2n,2n)}.
a(n) = (1/C(n,0) - 1/C(n,1) + ... + d/C(n,k))*L, where d = (-1)^k,k = [ n/2 ], L = LCM{C(n,0), C(n,1),..., C(n,n)}.A025536
a(n) = (1/C(n,0) - 1/C(n,1) + ... + d/C(n,k))*L, where d = (-1)^k,k = [ n/2 ], L = LCM{C(n,0), C(n,1),..., C(n,n)}.
a(n) = (1/s(1) + 1/s(2) + ... + 1/s(n+1)) * LCM{1, 2, ..., n}, where s(k) = LCM{1,2,...,k}/k = A002944(k).A025537
a(n) = (1/s(1) + 1/s(2) + ... + 1/s(n+1)) * LCM{1, 2, ..., n}, where s(k) = LCM{1,2,...,k}/k = A002944(k).
a(n) = (1/s(1) - 1/s(2) + ... + d/s(n+1)) * LCM{1, 2, ..., n}, where d = (-1)^n, s = A002944, i.e., s(k) = LCM of row k of Pascal's triangle.A025538
a(n) = (1/s(1) - 1/s(2) + ... + d/s(n+1)) * LCM{1, 2, ..., n}, where d = (-1)^n, s = A002944, i.e., s(k) = LCM of row k of Pascal's triangle.
a(n) = (Sum{1/C(i,j)})*LCM{C(i,j)}, 0 <= j <= i <= n.A025539
a(n) = (Sum{1/C(i,j)})*LCM{C(i,j)}, 0 <= j <= i <= n.
Least common multiple of {C(0,0), C(2,1), ..., C(2n,n)}.A025540
Least common multiple of {C(0,0), C(2,1), ..., C(2n,n)}.
a(n) = (1/C(0,0) + 1/C(2,1) + ... + 1/C(2n,n))*L, where L = LCM{C(0,0), C(2,1),..., C(2n,n)}.A025541
a(n) = (1/C(0,0) + 1/C(2,1) + ... + 1/C(2n,n))*L, where L = LCM{C(0,0), C(2,1),..., C(2n,n)}.
(1/binomial(0,0) - 1/binomial(2,1) + ... + d/binomial(2n,n))*L, where d = (-1)^n, L = LCM{binomial(0,0), binomial(2,1),..., binomial(2n,n)}.A025542
(1/binomial(0,0) - 1/binomial(2,1) + ... + d/binomial(2n,n))*L, where d = (-1)^n, L = LCM{binomial(0,0), binomial(2,1),..., binomial(2n,n)}.
Least common multiple of the first n composite numbers.A025543
Least common multiple of the first n composite numbers.
a(n) = sum of the exponents in the prime factorization of the least common multiple of the first n composite numbers.A025544
a(n) = sum of the exponents in the prime factorization of the least common multiple of the first n composite numbers.
a(n) = (1/4 + 1/6 + ... + 1/c(n))*LCM{4, 6, ..., c(n)}, where c(n) = n-th composite number.A025545
a(n) = (1/4 + 1/6 + ... + 1/c(n))*LCM{4, 6, ..., c(n)}, where c(n) = n-th composite number.
(1/4 - 1/6 + ... + d/c(n))*LCM{4, 6, ..., c(n)}, where d = (-1)^(n-1), c(n) = n-th composite number.A025546
(1/4 - 1/6 + ... + d/c(n))*LCM{4, 6, ..., c(n)}, where d = (-1)^(n-1), c(n) = n-th composite number.
Least common multiple of {1,3,5,...,2n-1}.A025547
Least common multiple of {1,3,5,...,2n-1}.
a(n) = sum of the exponents in the prime factorization of the least common multiple of {1,3,5,...,2n-1}.A025548
a(n) = sum of the exponents in the prime factorization of the least common multiple of {1,3,5,...,2n-1}.
a(n) = (2n-1)!!/lcm{1,3,5,...,2n-1}.A025549
a(n) = (2n-1)!!/lcm{1,3,5,...,2n-1}.
a(n) = ( 1/1 + 1/3 + 1/5 + ... + 1/(2*n-1) )*LCM(1, 3, 5, ..., 2*n-1).A025550
a(n) = ( 1/1 + 1/3 + 1/5 + ... + 1/(2*n-1) )*LCM(1, 3, 5, ..., 2*n-1).
a(n) = 3^n*(3^n + 1)/2.A025551
a(n) = 3^n*(3^n + 1)/2.
LCM of {C(0,0), C(1,0), ..., C(n, floor(n/2))}.A025552
LCM of {C(0,0), C(1,0), ..., C(n, floor(n/2))}.
a(n) = (Sum_{i=0..n-1} 1/b(i)) * LCM{b(i): i=0..n-1}, where b(i) = C(i,floor(i/2)).A025553
a(n) = (Sum_{i=0..n-1} 1/b(i)) * LCM{b(i): i=0..n-1}, where b(i) = C(i,floor(i/2)).
a(n) = (Sum_{i=0..n-1} (-1)^i/b(i)) * LCM{b(i): i=0..n-1}, where b(i) = C(i,floor(i/2)).A025554
a(n) = (Sum_{i=0..n-1} (-1)^i/b(i)) * LCM{b(i): i=0..n-1}, where b(i) = C(i,floor(i/2)).
Least common multiple (or LCM) of first n positive triangular numbers (A000217).A025555
Least common multiple (or LCM) of first n positive triangular numbers (A000217).
a(n) = sum of the exponents in the prime factorization of LCM{1,3,6,...,C(n+1,2)}.A025556
a(n) = sum of the exponents in the prime factorization of LCM{1,3,6,...,C(n+1,2)}.
a(n) = (n+1)!/LCM{1,3,6,...,C(n+1,2)}.A025557
a(n) = (n+1)!/LCM{1,3,6,...,C(n+1,2)}.
a(n) = (n/(n+1)) * lcm(1,2,...,n+1).A025558
a(n) = (n/(n+1)) * lcm(1,2,...,n+1).
(1/1 - 1/3 + 1/6 + ... + d/C(n+1,2))*LCM{1,3,6,...,C(n+1,2)}, where d = (-1)^n.A025559
(1/1 - 1/3 + 1/6 + ... + d/C(n+1,2))*LCM{1,3,6,...,C(n+1,2)}, where d = (-1)^n.
a(n) = LCM{1, C(n-1,1), C(n-2,2), ..., C(n-[ n/2 ],[ n/2 ])}.A025560
a(n) = LCM{1, C(n-1,1), C(n-2,2), ..., C(n-[ n/2 ],[ n/2 ])}.