A375432 - OEIS

%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