Sequences

Number of digits in the base 3 representation of n-th Fibonacci number.

Number of terms in base 4 representation of n-th Fibonacci number.

Number of terms in base 5 representation of Fibonacci(n).

Number of digits in the base-2 representation of 3^n.

Number of digits in base-3 representation of 2^n.

A molecule is a row of atoms joined together by bonds; each atom has a valence (e.g., 1-3=2 is a molecule with 3 atoms); a(n) is the number of molecules with n atoms and different valencies from 1 to n.

Maximum number of K4's (complete 4 graphs) a graph can contain if it contains at most n distinct K3's (triangles).

Expansion of 1/(1-4*x)^(7/2).

Partition numbers mod 11.

Expansion of 1/(1-4*x)^(9/2).

Triangle read by rows: T(m,n) = number of solutions to 1 <= a(1) < a(2) < ... < a(m) <= n, where gcd( a(1), a(2), ..., a(m), n) = 1.

Expansion of 1/(1-4*x)^(11/2).

Expansion of (1-4*x)^(11/2).

Expansion of 1/(1-4*x)^(13/2).

Expansion of (1-4*x)^(13/2).

Expansion of 1/(1-4*x)^(15/2).

Expansion of (1-4*x)^(15/2).

Expansion of 1/(1-4*x)^(17/2).

Expansion of (1-4*x)^(17/2).

Expansion of 1/(1-4*x)^(19/2).

Expansion of (1-4*x)^(19/2).

Expansion of 1/(1-4*x)^(21/2).

Expansion of (1-4*x)^(21/2).

Greatest k such that (k-th prime) < (4 times n-th prime).

Greatest k such that (k-th prime) < (5 times n-th prime).

Greatest k such that (k-th prime) < (6 times n-th prime).

Greatest k such that (k-th prime) < (7 times n-th prime).

Greatest k such that (k-th prime) < (8 times n-th prime).

Greatest k such that (k-th prime) < (9 times n-th prime).

Greatest k such that (k-th prime) < (10 times n-th prime).

Main diagonal of Wythoff array: w(n,n)=[ n*tau ]F(n+1)+(n-1)F(n), where tau=(1+sqrt(5))/2, F(n) = Fibonacci numbers.

First column of 3rd-order Zeckendorf array A136189.

a(2n+1) = |a(2n) - a(2n-1)|, a(2n) = a(n) + a(n-1).

a(2n+1) = |a(2n) - a(2n-1)|, a(2n) = a(n) + a(n-1), a(0) = -1.

a(2n+1) = |a(2n) - a(2n-1)|, a(2n) = a(n) + a(n-1).

a(n) is the smallest number k such that A002487(k) = n.

Least k such that A(k) = n, where A( ) is sequence A020943.

Least k such that b(k) = n, where b( ) is sequence A020944.

Least k such that A(k) = n, where A( ) is sequence A020945.

a(n) = k-1, where k is smallest number such that A002487(k) = n.

a(2n+1)=a(n), a(2n)=a(n)+a(n-1).

a(2n+1)=a(n), a(2n)=a(n)+a(n-1).

Least k such that A020951(k) = n.

Least k such that A020952(k) = n.

a(n) = n^(2^n - n - 1).

a(n) = Sum_{k>=1} floor(tau^(n-k)) where tau is A001622.

a(n) = Sum_{k >= 1} floor(2*tau^(n-k)).

a(n) = Sum_{k >= 1} floor(3*tau^(n-k)).

a(n) = Sum_{k>=1} floor(n*phi^(1-k)).

a(n) = Sum_{k >= 1} floor(n*phi^(2-k)).