Sequences

392,541 sequences

Number of terms in n-th derivative of a function composed with itself 3 times.A022811
Number of terms in n-th derivative of a function composed with itself 3 times.
Number of terms in n-th derivative of a function composed with itself 4 times.A022812
Number of terms in n-th derivative of a function composed with itself 4 times.
Number of terms in n-th derivative of a function composed with itself 5 times.A022813
Number of terms in n-th derivative of a function composed with itself 5 times.
Number of terms in n-th derivative of a function composed with itself 6 times.A022814
Number of terms in n-th derivative of a function composed with itself 6 times.
Number of terms in 5th derivative of a function composed with itself n times.A022815
Number of terms in 5th derivative of a function composed with itself n times.
Number of terms in 6th derivative of a function composed with itself n times.A022816
Number of terms in 6th derivative of a function composed with itself n times.
Number of terms in 7th derivative of a function composed with itself n times.A022817
Number of terms in 7th derivative of a function composed with itself n times.
Square array read by antidiagonals: A(n,k) = number of terms in the n-th derivative of a function composed with itself k times (n, k >= 1).A022818
Square array read by antidiagonals: A(n,k) = number of terms in the n-th derivative of a function composed with itself k times (n, k >= 1).
a(n) = floor(1/(n-1) + 2/(n-2) + 3/(n-3) + ... + (n-1)/1).A022819
a(n) = floor(1/(n-1) + 2/(n-2) + 3/(n-3) + ... + (n-1)/1).
[ n/1 ] - [ (n-1)/2 ] + [ (n-2)/3 ] - ... + ((-1)^n)[ 2/(n-1) ].A022820
[ n/1 ] - [ (n-1)/2 ] + [ (n-2)/3 ] - ... + ((-1)^n)[ 2/(n-1) ].
[ (n+1)/(n-1) ] + [ (n+2)/(n-2) ] + ... + [ (2n-1)/1 ].A022821
[ (n+1)/(n-1) ] + [ (n+2)/(n-2) ] + ... + [ (2n-1)/1 ].
a(n) = [ (n+2)/(n-1) ] + [ (n+4)/(n-2) ] + ... + [ (3n-2)/1 ].A022822
a(n) = [ (n+2)/(n-1) ] + [ (n+4)/(n-2) ] + ... + [ (3n-2)/1 ].
a(n) = [ (2n+1)/(n-1) ] + [ (2n+2)/(n-2) ] + ... + [ (3n-1)/1 ].A022823
a(n) = [ (2n+1)/(n-1) ] + [ (2n+2)/(n-2) ] + ... + [ (3n-1)/1 ].
a(n) = [ (2n+2)/(n-1) ] + [ (2n+4)/(n-2) ] + ... + [ (4n-2)/1 ].A022824
a(n) = [ (2n+2)/(n-1) ] + [ (2n+4)/(n-2) ] + ... + [ (4n-2)/1 ].
a(n) = a([ n/2 ]) + a([ n/3 ]) + . . . + a([ n/n ]) for n > 1, a(1) = 1.A022825
a(n) = a([ n/2 ]) + a([ n/3 ]) + . . . + a([ n/n ]) for n > 1, a(1) = 1.
a(n) = a([ (n+1)/2 ]) + a([ (n+1)/3 ]) + . . . + a([ (n+1)/n ]).A022826
a(n) = a([ (n+1)/2 ]) + a([ (n+1)/3 ]) + . . . + a([ (n+1)/n ]).
a(n) = absolute value of ( a([ n/2 ]) - a([ n/3 ]) + ... + ((-1)^n)a([ n/n ]) ).A022827
a(n) = absolute value of ( a([ n/2 ]) - a([ n/3 ]) + ... + ((-1)^n)a([ n/n ]) ).
a(n) = absolute value of ( a([ (n+1)/2 ]) - a([ (n+1)/3 ])+...+((-1)^n)a([ (n+1)/n ]) ).A022828
a(n) = absolute value of ( a([ (n+1)/2 ]) - a([ (n+1)/3 ])+...+((-1)^n)a([ (n+1)/n ]) ).
a(n) = a([ .5 + n/2 ]) + a([ .5 + n/3 ]) + ... + a([ .5 + n/n ]).A022829
a(n) = a([ .5 + n/2 ]) + a([ .5 + n/3 ]) + ... + a([ .5 + n/n ]).
a(n) = -[ n/2 ] + a([ n/2 ]) + a([ n/3 ]) + . . . + a([ n/n ]).A022830
a(n) = -[ n/2 ] + a([ n/2 ]) + a([ n/3 ]) + . . . + a([ n/n ]).
a(n) = c(1)p(1) + ... + c(n)p(n), where c(i) = 1 if a(i-1) <= p(i) and c(i) = -1 if a(i-1) > p(i), for i = 1,...,n (p(i) = primes).A022831
a(n) = c(1)p(1) + ... + c(n)p(n), where c(i) = 1 if a(i-1) <= p(i) and c(i) = -1 if a(i-1) > p(i), for i = 1,...,n (p(i) = primes).
Duplicate of A008348.A022832
Duplicate of A008348.
a(0)=2; thereafter a(n) = a(n-1) + prime(n) if a(n-1) < prime(n), otherwise a(n) = a(n-1) - prime(n). Cf. A008348.A022833
a(0)=2; thereafter a(n) = a(n-1) + prime(n) if a(n-1) < prime(n), otherwise a(n) = a(n-1) - prime(n). Cf. A008348.
a(n) = c(1)p(3) + ... + c(n)p(n+2), where c(i) = 1 if a(i-1) <= p(i+2) and c(i) = -1 if a(i-1) > p(i+2) (p(i) = primes).A022834
a(n) = c(1)p(3) + ... + c(n)p(n+2), where c(i) = 1 if a(i-1) <= p(i+2) and c(i) = -1 if a(i-1) > p(i+2) (p(i) = primes).
a(n) = c(1)p(3) + ... + c(n)p(n+2), where c(i) = 1 if a(i-1) < p(i+2) and c(i) = -1 if a(i-1) >= p(i+2) (p(i) = primes).A022835
a(n) = c(1)p(3) + ... + c(n)p(n+2), where c(i) = 1 if a(i-1) < p(i+2) and c(i) = -1 if a(i-1) >= p(i+2) (p(i) = primes).
a(n) = c(1)*p(0) + ... + c(n)*p(n-1), where c(i) = 1 if a(i-1) <= p(i-1) and c(i) = -1 if a(i-1) > p(i-1) (with p(0) = 1 and p(i) a prime for i >= 1).A022836
a(n) = c(1)*p(0) + ... + c(n)*p(n-1), where c(i) = 1 if a(i-1) <= p(i-1) and c(i) = -1 if a(i-1) > p(i-1) (with p(0) = 1 and p(i) a prime for i >= 1).
a(n) = c(0)*p(0) + ... + c(n)*p(n), where c(i) = 1 if a(i-1) < p(i) and c(i) = -1 if a(i-1) >= p(i) (p(0) = 1, p(i) = prime(i)).A022837
a(n) = c(0)*p(0) + ... + c(n)*p(n), where c(i) = 1 if a(i-1) < p(i) and c(i) = -1 if a(i-1) >= p(i) (p(0) = 1, p(i) = prime(i)).
Beatty sequence for sqrt(3); complement of A054406.A022838
Beatty sequence for sqrt(3); complement of A054406.
Beatty sequence for sqrt(5).A022839
Beatty sequence for sqrt(5).
Beatty sequence for sqrt(6).A022840
Beatty sequence for sqrt(6).
Beatty sequence for sqrt(7).A022841
Beatty sequence for sqrt(7).
Beatty sequence for sqrt(8).A022842
Beatty sequence for sqrt(8).
Beatty sequence for e: a(n) = floor(n*e).A022843
Beatty sequence for e: a(n) = floor(n*e).
a(n) = floor(n*Pi).A022844
a(n) = floor(n*Pi).
Expansion of 1/((1-x)*(1-5*x)*(1-9*x)*(1-10*x)).A022845
Expansion of 1/((1-x)*(1-5*x)*(1-9*x)*(1-10*x)).
Nearest integer to n*sqrt(2).A022846
Nearest integer to n*sqrt(2).
Integer nearest n*sqrt(3).A022847
Integer nearest n*sqrt(3).
Integer nearest nx, where x = sqrt(5).A022848
Integer nearest nx, where x = sqrt(5).
Integer nearest nx, where x = sqrt(6).A022849
Integer nearest nx, where x = sqrt(6).
Integer nearest n*x, where x = sqrt(7).A022850
Integer nearest n*x, where x = sqrt(7).
a(n) = integer nearest n*x, where x = sqrt(8).A022851
a(n) = integer nearest n*x, where x = sqrt(8).
Integer nearest n * e, where e is the natural log base.A022852
Integer nearest n * e, where e is the natural log base.
a(n) = integer nearest n*Pi.A022853
a(n) = integer nearest n*Pi.
a(n) = [ a(n-1)/a(1) + a(n-1)/a(2) + ... + a(n-1)/a(n-1) ] for n >= 3, with initial terms 1,1.A022854
a(n) = [ a(n-1)/a(1) + a(n-1)/a(2) + ... + a(n-1)/a(n-1) ] for n >= 3, with initial terms 1,1.
a(n) = [ a(n-1)/a(1) ] + [ a(n-1)/a(2) ] + ... + [ a(n-1)/a(n-1) ] for n >= 3, with initial terms 1,1.A022855
a(n) = [ a(n-1)/a(1) ] + [ a(n-1)/a(2) ] + ... + [ a(n-1)/a(n-1) ] for n >= 3, with initial terms 1,1.
a(n) = n-2 + Sum_{i = 1..n-2} (a(i+1) mod a(i)) for n >= 3 with a(1) = a(2) = 1.A022856
a(n) = n-2 + Sum_{i = 1..n-2} (a(i+1) mod a(i)) for n >= 3 with a(1) = a(2) = 1.
a(n) = [ a(n-1)/a(1) + a(n-2)/a(2) + ... + a(1)/a(n-1) ], for n >= 3.A022857
a(n) = [ a(n-1)/a(1) + a(n-2)/a(2) + ... + a(1)/a(n-1) ], for n >= 3.
a(n) = [ a(n-1)/a(1) ] + [ a(n-2)/a(2) ] + ... + [ a(1)/a(n-1) ], for n >= 3.A022858
a(n) = [ a(n-1)/a(1) ] + [ a(n-2)/a(2) ] + ... + [ a(1)/a(n-1) ], for n >= 3.
a(n) = [ a(n-1)/a(1) + a(n-3)/a(3) + a(n-5)/a(5) + ... ], for n >= 3.A022859
a(n) = [ a(n-1)/a(1) + a(n-3)/a(3) + a(n-5)/a(5) + ... ], for n >= 3.
a(n) = [ a(n-1)/a(1) ] + [ a(n-3)/a(3) ] + [ a(n-5)/a(5) ] + ..., for n >= 3.A022860
a(n) = [ a(n-1)/a(1) ] + [ a(n-3)/a(3) ] + [ a(n-5)/a(5) ] + ..., for n >= 3.