A307294 -id:A307294 - cp's OEIS frontend

A307295 If n is even, a(n) = A001950(n/2+1), otherwise a(n) = A001950((n-1)/2+1) + 1.

2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 23, 24, 26, 27, 28, 29, 31, 32, 34, 35, 36, 37, 39, 40, 41, 42, 44, 45, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 60, 61, 62, 63, 65, 66, 68, 69, 70, 71, 73, 74, 75, 76, 78, 79, 81, 82, 83, 84, 86, 87, 89, 90, 91, 92, 94, 95, 96, 97, 99, 100, 102, 103, 104, 105

Offset: 0

N. J. A. Sloane, Apr 12 2019

nonn

It follows from the definition that a(2i+1) = a(2i)+1 for all i.
From Jeffrey Shallit, Jun 06 2021: (Start)
This sequence consists of the nonzero distances between occurrences of 1 in the Fibonacci word A003849 (easily provable with the Walnut theorem-prover).
Alternatively, these are the positive n such that A003849(n-1) = 1 or A003849(n-2) = 1 (again, easily provable with the Walnut theorem-prover). (End)

Eric Friedman, Scott M. Garrabrant, Ilona K. Phipps-Morgan, A. S. Landsberg and Urban Larsson, Geometric analysis of a generalized Wythoff game, in Games of no Chance 5, MSRI publ. Cambridge University Press, date? [See Omega, a few lines below Table 2.]

Cf. A000201, A001950, A307294.

from math import isqrt
def A307295(n): return ((m:=(n>>1)+1)+isqrt(5*m**2)>>1)+m+(n&1) # Chai Wah Wu, Aug 10 2022

cp's OEIS Frontend

A307295 If n is even, a(n) = A001950(n/2+1), otherwise a(n) = A001950((n-1)/2+1) + 1.

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