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

0,1

Comments

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)

References

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.]

Links

Table of n, a(n) for n=0..79.

Prog

(Python)
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

Crossrefs

Cf. A000201, A001950, A307294.

Sequence in context: A304364 A336590 A000452 * A047587 A285420 A028737

Adjacent sequences: A307292 A307293 A307294 * A307296 A307297 A307298

Keyword

nonn

Author

N. J. A. Sloane, Apr 12 2019

Status

approved