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%I #24 Aug 11 2022 03:19:45
%S 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,
%T 35,36,37,39,40,41,42,44,45,47,48,49,50,52,53,54,55,57,58,60,61,62,63,
%U 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
%N If n is even, a(n) = A001950(n/2+1), otherwise a(n) = A001950((n-1)/2+1) + 1.
%C It follows from the definition that a(2i+1) = a(2i)+1 for all i.
%C From _Jeffrey Shallit_, Jun 06 2021: (Start)
%C This sequence consists of the nonzero distances between occurrences of 1 in the Fibonacci word A003849 (easily provable with the Walnut theorem-prover).
%C 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)
%D 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.]
%o (Python)
%o from math import isqrt
%o def A307295(n): return ((m:=(n>>1)+1)+isqrt(5*m**2)>>1)+m+(n&1) # _Chai Wah Wu_, Aug 10 2022
%Y Cf. A000201, A001950, A307294.
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Apr 12 2019
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