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%I #7 Aug 16 2024 21:21:30
%S 8,24,27,32,40,54,56,64,72,88,96,104,108,120,125,135,136,152,160,168,
%T 184,189,192,200,216,224,232,243,248,250,256,264,270,280,288,296,297,
%U 312,320,328,343,344,351,352,360,375,376,378,392,408,416,424,440,448,456
%N Numbers k such that A375428(k) > A375430(k).
%C First differs from A374590 at n = 31.
%C For numbers k that are not in this sequence A375428(k) = A375430(k).
%C Numbers k such that A051903(k)+1 is not of the form Fibonacci(m)-1, m >= 3.
%C The asymptotic density of this sequence is 1 - 1/zeta(2) - Sum_{k>=4} (1/zeta(Fibonacci(k)) - 1/zeta(Fibonacci(k)-1)) = 0.12330053981922224451... .
%H Amiram Eldar, <a href="/A375432/b375432.txt">Table of n, a(n) for n = 1..10000</a>
%e 8 is a term since A375428(8) = 3 > 2 = A375430(8).
%t fibQ[n_] := n >= 2 && Or @@ IntegerQ /@ Sqrt[5*n^2 + {-4, 4}]; Select[Range[300], !fibQ[Max[FactorInteger[#][[;;, 2]]] + 1] &]
%o (PARI) isfib(n) = n >= 2 && (issquare(5*n^2-4) || issquare(5*n^2+4));
%o is(n) = n > 1 && !isfib(vecmax(factor(n)[,2]) + 1);
%Y Cf. A000045, A000071, A051903, A374590, A375428, A375430.
%K nonn,easy,base
%O 1,1
%A _Amiram Eldar_, Aug 15 2024