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 A190723 #25 Apr 14 2020 11:45:50
%S A190723 1,2,4,8,9,11,15,19,20,22,26,27,29,33,37,38,40,44,48,49,51,55,56,58,
%T A190723 62,66,67,69,73,74,76,80,84,85,87,91,95,96,98,102,103,105,109,113,114,
%U A190723 116,120,124,125,127,131,132,134,138,142,143,145,149,150,152,156
%N A190723 Numbers m for which A055778(m) > A055778(m-1).
%C A190723 The sequence (a(n+1)-1) = 1,3,7,8,10,... is the union of two generalized Beatty sequences, namely (floor(n*phi)+2*n) = A003231, and the sequence (4*floor(n*phi)+3*n+1), the latter with offset 0. For a proof see my paper "Points of increase...". - _Michel Dekking_, Apr 01 2020
%H A190723 Michael De Vlieger, <a href="/A190723/b190723.txt">Table of n, a(n) for n = 1..10000</a>
%H A190723 Michel Dekking, <a href="https://arxiv.org/abs/2003.14125">Points of increase of the sum of digits function of the base phi expansion</a>, arXiv:2003.14125 [math.CO], 2020.
%F A190723 a(n) = 1 + Sum_{k=1..n-1} x(k), where x is the unique fixed point of the morphism 1->12, 2->4, 4->1244 on the alphabet {1,2,4}. - _Michel Dekking_, Apr 01 2020
%t A190723 Block[{nn = 160, k}, k = 2 Ceiling[Log[GoldenRatio, nn]]; Position[Differences@ Array[Total@ First@ RealDigits[#, GoldenRatio, k] &, nn, 0], _?(# > 0 &)][[All, 1]]] (* _Michael De Vlieger_, Apr 02 2020, after _T. D. Noe_ at A055778 *)
%Y A190723 Cf. A055778, A190720, A190721, A003231. The morphism in the Formula is a change of alphabet of the morphism generating A284749.
%K A190723 nonn
%O A190723 1,2
%A A190723 _Carmine Suriano_, May 17 2011