A026355 a(n) = least k such that s(k) = n+1, where s = A026354.

1, 2, 3, 5, 6, 8, 10, 11, 13, 14, 16, 18, 19, 21, 23, 24, 26, 27, 29, 31, 32, 34, 35, 37, 39, 40, 42, 44, 45, 47, 48, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 73, 74, 76, 78, 79, 81, 82, 84, 86, 87, 89, 90, 92, 94, 95, 97, 99, 100, 102, 103, 105, 107, 108, 110

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

Let f(1)=1, f(2)=q and f(k+2) = f(k+1)+f(k)-n; a(n) is the smallest positive integer q such that f(k) -> infinity as k -> infinity. - Benoit Cloitre, Aug 04 2002

Links

• J. H. Conway and N. J. A. Sloane, Notes on the Para-Fibonacci and related sequences

Crossrefs

Cf. A000201, A005614, A026351. Different from A007067.

Programs

Python

from math import isqrt
def A026355(n): return (n-1+isqrt(5*(n-1)**2)>>1)+2 if n else 1 # Chai Wah Wu, Aug 25 2022

Formula

For n>0, a(n) = floor((n-1)*phi) + 2, where phi=(1+sqrt(5))/2.

Recurrences: a(n+1) = a(n)+(3 + sign(phi*n-a(n)))/2 for n>=0. Also a(n+1) = a(n) + 1 + A005614(n-2) for n>=2. - Benoit Cloitre, Aug 04 2002