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 A384947 #34 Jun 20 2025 10:45:08
%S A384947 15,18,36,39,41,47,49,52,91,94,96,102,103,104,107,109,123,125,128,130,
%T A384947 136,138,141,235,238,240,246,247,248,251,252,253,267,268,269,272,273,
%U A384947 274,277,280,281,282,285,287,303,306,322,324,327,328
%N A384947 Positive integers m for which A183136(m) != f(m), where f(m) = floor( (m*(m+1)/2)/phi - m/2 + 1/(2*phi) ) and phi = (1+sqrt(5))/2 is the golden ratio.
%C A384947 f(m) is an approximation to A183136(m) = Sum_{k=1..m} floor(k/phi) based on assuming the floor in each term decreases it by 1/2 from what is otherwise a triangular sum; and further offset + 1/(2*phi) in f(m) chosen to improve the accuracy of this approximation.
%C A384947 The actual values of frac(k/phi) can differ from 1/2 each by a net amount which is enough to make m a term of this sequence.
%H A384947 Paolo Xausa, <a href="/A384947/b384947.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Hoang Xuan Thanh)
%e A384947 41 is term, because A183136(41) = 512 != 511 = floor(((41^2+1)*phi - 41) / (2*phi^2)).
%t A384947 PositionIndex[MapIndexed[# != Floor[PolygonalNumber[#2[[1]]]/GoldenRatio - #2[[1]]/2 + 1/(2*GoldenRatio)] &, Accumulate[Floor[Range[500]/GoldenRatio]]]][True] (* _Paolo Xausa_, Jun 20 2025 *)
%Y A384947 Cf. A183136, A001622, A060143.
%K A384947 nonn
%O A384947 1,1
%A A384947 _Hoang Xuan Thanh_, Jun 13 2025