Sequences

392,541 sequences

Positions of odd numbers in A004431 (sums of 2 distinct nonzero squares).A024511
Positions of odd numbers in A004431 (sums of 2 distinct nonzero squares).
Position of 1 + n^2 in A004431 (sums of 2 distinct nonzero squares).A024512
Position of 1 + n^2 in A004431 (sums of 2 distinct nonzero squares).
a(n) = position of n^2 + (n+1)^2 in A004431 (sums of 2 distinct nonzero squares).A024513
a(n) = position of n^2 + (n+1)^2 in A004431 (sums of 2 distinct nonzero squares).
Positions of primes in A004431 (sums of 2 distinct nonzero squares).A024514
Positions of primes in A004431 (sums of 2 distinct nonzero squares).
Positions of even numbers in A000404 (sums of 2 nonzero squares).A024515
Positions of even numbers in A000404 (sums of 2 nonzero squares).
Positions of odd numbers in A000404 (sums of 2 nonzero squares).A024516
Positions of odd numbers in A000404 (sums of 2 nonzero squares).
Position of 2*n^2 in A000404 (sums of 2 nonzero squares).A024517
Position of 2*n^2 in A000404 (sums of 2 nonzero squares).
a(n) = position of 1 + n^2 in A000404 (sums of 2 nonzero squares).A024518
a(n) = position of 1 + n^2 in A000404 (sums of 2 nonzero squares).
Position of n^2 + (n+1)^2 in A000404 (sums of 2 nonzero squares).A024519
Position of n^2 + (n+1)^2 in A000404 (sums of 2 nonzero squares).
Positions of primes in A000404 (sums of 2 nonzero squares).A024520
Positions of primes in A000404 (sums of 2 nonzero squares).
Erroneous version of A014284.A024521
Erroneous version of A014284.
a(n) = 2nd elementary symmetric function of {1, prime(1), prime(2), ..., prime(n-1)}, where prime(0) = 1.A024522
a(n) = 2nd elementary symmetric function of {1, prime(1), prime(2), ..., prime(n-1)}, where prime(0) = 1.
a(n) = 3rd elementary symmetric function of {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.A024523
a(n) = 3rd elementary symmetric function of {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.
4th elementary symmetric function of {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.A024524
4th elementary symmetric function of {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.
a(n) = 1^2 + prime(1)^2 + prime(2)^2 + ... + prime(n)^2.A024525
a(n) = 1^2 + prime(1)^2 + prime(2)^2 + ... + prime(n)^2.
a(n) = Sum_{0 <= i < j <= n} (prime(j) - prime(i))^2, where prime(0) = 1.A024526
a(n) = Sum_{0 <= i < j <= n} (prime(j) - prime(i))^2, where prime(0) = 1.
a(n) = sum of cubes of p(j) - p(i), for 0 <= i < j <= n, where p(0) = 1.A024527
a(n) = sum of cubes of p(j) - p(i), for 0 <= i < j <= n, where p(0) = 1.
a(n) = n-th elementary symmetric function of {1, prime(1), prime(2), ..., prime(n)}.A024528
a(n) = n-th elementary symmetric function of {1, prime(1), prime(2), ..., prime(n)}.
a(n) = s(1)*s(2)*...*s(n)*(1/s(1) - 1/s(2) + ... + c/s(n)), where s(1) = 1, s(k) = p(k-1) for k >= 2 and c = (-1)^(n+1).A024529
a(n) = s(1)*s(2)*...*s(n)*(1/s(1) - 1/s(2) + ... + c/s(n)), where s(1) = 1, s(k) = p(k-1) for k >= 2 and c = (-1)^(n+1).
Numerator of -Sum_{k=1..n} (-1)^k / prime(k).A024530
Numerator of -Sum_{k=1..n} (-1)^k / prime(k).
a(n) = [ (2nd elementary symmetric function of P(n))/(first elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.A024531
a(n) = [ (2nd elementary symmetric function of P(n))/(first elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.
a(n) = [ (3rd elementary symmetric function of P(n))/(first elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.A024532
a(n) = [ (3rd elementary symmetric function of P(n))/(first elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.
[ (4th elementary symmetric function of P(n))/(first elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.A024533
[ (4th elementary symmetric function of P(n))/(first elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.
a(n) = [ (3rd elementary symmetric function of P(n))/(2nd elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.A024534
a(n) = [ (3rd elementary symmetric function of P(n))/(2nd elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.
[ (4th elementary symmetric function of P(n))/(2nd elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.A024535
[ (4th elementary symmetric function of P(n))/(2nd elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.
[ (4th elementary symmetric function of P(n))/(3rd elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, p(0) = 1.A024536
[ (4th elementary symmetric function of P(n))/(3rd elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, p(0) = 1.
a(n) = floor( a(n-1)/(sqrt(2) - 1) ), with a(0) = 1.A024537
a(n) = floor( a(n-1)/(sqrt(2) - 1) ), with a(0) = 1.
a(n) = [ n/{n*sqrt(2)} ], where {x} := x - [ x ].A024538
a(n) = [ n/{n*sqrt(2)} ], where {x} := x - [ x ].
a(n) = [ 1/{n*sqrt(2)} ], where {x} := x - [ x ].A024539
a(n) = [ 1/{n*sqrt(2)} ], where {x} := x - [ x ].
a(n) = Sum_{k=1..n} floor( 1/{k*sqrt(2)} ), where {x} := x - floor(x).A024540
a(n) = Sum_{k=1..n} floor( 1/{k*sqrt(2)} ), where {x} := x - floor(x).
[ sum of 1/{k*sqrt(2)} ], k = 1,2,...,n, where {x} := x - [ x ].A024541
[ sum of 1/{k*sqrt(2)} ], k = 1,2,...,n, where {x} := x - [ x ].
Lower bound on cumulative mean of distances between cards after n shuffles in A024222.A024542
Lower bound on cumulative mean of distances between cards after n shuffles in A024222.
[ n/{n/sqrt(2)} ], where {x} := x - [ x ].A024543
[ n/{n/sqrt(2)} ], where {x} := x - [ x ].
a(n) = [ 1/{n/sqrt(2)} ], where {x} := x - [ x ].A024544
a(n) = [ 1/{n/sqrt(2)} ], where {x} := x - [ x ].
a(n) = Sum_{k=1..n} floor( 1/{k/sqrt(2)} ), where {x} := x - floor(x).A024545
a(n) = Sum_{k=1..n} floor( 1/{k/sqrt(2)} ), where {x} := x - floor(x).
a(n) = [ sum of 1/{k/sqrt(2)} ], k = 1,2,...,n, where {x} := x - [ x ].A024546
a(n) = [ sum of 1/{k/sqrt(2)} ], k = 1,2,...,n, where {x} := x - [ x ].
a(n) = [ n/{n*sqrt(3)} ], where {x} := x - [ x ].A024547
a(n) = [ n/{n*sqrt(3)} ], where {x} := x - [ x ].
[ 1/{n*sqrt(3)} ], where {x} := x - [ x ].A024548
[ 1/{n*sqrt(3)} ], where {x} := x - [ x ].
Sum of [ 1/{k*sqrt(3)} ], k = 1,2,...,n, where {x} := x - [ x ].A024549
Sum of [ 1/{k*sqrt(3)} ], k = 1,2,...,n, where {x} := x - [ x ].
[ Sum of 1/{k*sqrt(3)} ], k = 1,2,...,n, where {x} := x - [ x ].A024550
[ Sum of 1/{k*sqrt(3)} ], k = 1,2,...,n, where {x} := x - [ x ].
a(n) = floor(a(n-1)/(sqrt(5) - 2)) for n > 0 and a(0) = 1.A024551
a(n) = floor(a(n-1)/(sqrt(5) - 2)) for n > 0 and a(0) = 1.
a(n) = [ n/{n*sqrt(5)} ], where {x} := x - [ x ].A024552
a(n) = [ n/{n*sqrt(5)} ], where {x} := x - [ x ].
[ 1/{n*sqrt(5)} ], where {x} := x - [ x ].A024553
[ 1/{n*sqrt(5)} ], where {x} := x - [ x ].
a(n) = Sum_{k=1..n} floor( 1/{k*sqrt(5)} ), where {x} := x - floor(x).A024554
a(n) = Sum_{k=1..n} floor( 1/{k*sqrt(5)} ), where {x} := x - floor(x).
a(n) = [ sum of 1/{k*sqrt(5)} ], k = 1,2,...,n, where {x} := x - [ x ].A024555
a(n) = [ sum of 1/{k*sqrt(5)} ], k = 1,2,...,n, where {x} := x - [ x ].
Odd squarefree composite numbers.A024556
Odd squarefree composite numbers.
a(n) = [ a(n-1)/(sqrt(6) - 2) ], where a(0) = 1.A024557
a(n) = [ a(n-1)/(sqrt(6) - 2) ], where a(0) = 1.
a(n) = [ n/{n*sqrt(6)} ], where {x} := x - [ x ].A024558
a(n) = [ n/{n*sqrt(6)} ], where {x} := x - [ x ].
a(n) = [ 1/{n*sqrt(6)} ], where {x} := x - [ x ].A024559
a(n) = [ 1/{n*sqrt(6)} ], where {x} := x - [ x ].
a(n) = Sum_{k=1..n} floor(1/{k*sqrt(6)}) where {x} := x - floor(x).A024560
a(n) = Sum_{k=1..n} floor(1/{k*sqrt(6)}) where {x} := x - floor(x).