This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A307295 #24 Aug 11 2022 03:19:45 %S A307295 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 A307295 35,36,37,39,40,41,42,44,45,47,48,49,50,52,53,54,55,57,58,60,61,62,63, %U A307295 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 A307295 If n is even, a(n) = A001950(n/2+1), otherwise a(n) = A001950((n-1)/2+1) + 1. %C A307295 It follows from the definition that a(2i+1) = a(2i)+1 for all i. %C A307295 From _Jeffrey Shallit_, Jun 06 2021: (Start) %C A307295 This sequence consists of the nonzero distances between occurrences of 1 in the Fibonacci word A003849 (easily provable with the Walnut theorem-prover). %C A307295 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 A307295 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 A307295 (Python) %o A307295 from math import isqrt %o A307295 def A307295(n): return ((m:=(n>>1)+1)+isqrt(5*m**2)>>1)+m+(n&1) # _Chai Wah Wu_, Aug 10 2022 %Y A307295 Cf. A000201, A001950, A307294. %K A307295 nonn %O A307295 0,1 %A A307295 _N. J. A. Sloane_, Apr 12 2019