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 A356664 #14 Aug 28 2022 08:28:59
%S A356664 0,2,4,10,12,14,18,20,22,30,32,34,38,40,44,48,52,60,62,72,76,78,80,82,
%T A356664 92,94,100,104,116,120,126,130,132,134,138,140,142,144,146,148,152,
%U A356664 154,156,158,160,168,176,180,182,186,188,192,194,202,210,222,224,226,228,230,232
%N A356664 Numbers k such that A225205(k) is in A354549.
%C A356664 Numbers k such that floor(A225205(k)^2*phi) = A225204(k)^2, phi = A001622.
%C A356664 Even numbers k such that (A225204(k)^2+1)/A225205(k)^2 > phi.
%C A356664 Even k is a term in A356591 if and only k is in this sequence and {A225205(k)^2*phi} < phi^(-2), where {} denotes the fractional part; see the comments in A354513.
%C A356664 Conjecture: this and A356591 have the same natural density.
%H A356664 Jianing Song, <a href="/A356664/b356664.txt">Table of n, a(n) for n = 1..293</a>
%F A356664 A354549(n+1) = A225205(a(n)).
%e A356664 4 is a term because A225204(4) = 125 and A225205(4) = 159, and floor(125^2*phi) = 159^2.
%o A356664 (PARI) print1("0, "); my(cofr=A331692_vector_bits(1000), conv=matrix(2, #cofr)); conv[, 1]=[1, 1]~; conv[, 2]=[4, 3]~; for(n=3, #cofr, conv[, n]=cofr[n]*conv[, n-1]+conv[, n-2]; if(n%2 == 1 && (conv[1, n]^2+1)^2 - (conv[1, n]^2+1)*(conv[2, n]^2) - (conv[2, n]^2)^2 > 0, print1(n-1, ", ")))
%o A356664 \\ Here conv[1, n] = A225204(n-1), conv[2, n] = A225205(n-1), n odd implies conv[1, n]/conv[2, n] < sqrt((1+sqrt(5))/2); let A = conv[1, n]^2+1, B = conv[2, n]^2, then A^2 - A*B - B^2 > 0 implies A/B > (1+sqrt(5))/2
%o A356664 \\ Modified by _Jianing Song_, Aug 28 2022 according to _Kevin Ryde_'s program for A331692
%Y A356664 Cf. A001622, A225204, A225205, A354549, A354513, A356591.
%K A356664 nonn
%O A356664 1,2
%A A356664 _Jianing Song_, Aug 21 2022