A375432 Numbers k such that A375428(k) > A375430(k).

8, 24, 27, 32, 40, 54, 56, 64, 72, 88, 96, 104, 108, 120, 125, 135, 136, 152, 160, 168, 184, 189, 192, 200, 216, 224, 232, 243, 248, 250, 256, 264, 270, 280, 288, 296, 297, 312, 320, 328, 343, 344, 351, 352, 360, 375, 376, 378, 392, 408, 416, 424, 440, 448, 456

Offset: 1

Author

Amiram Eldar, Aug 15 2024

Keywords

• nonn
• easy
• base

Comments

First differs from A374590 at n = 31.

For numbers k that are not in this sequence A375428(k) = A375430(k).

Numbers k such that A051903(k)+1 is not of the form Fibonacci(m)-1, m >= 3.

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... .

Examples

			8 is a term since A375428(8) = 3 > 2 = A375430(8).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A000071, A051903, A374590, A375428, A375430.

Programs

Mathematica

fibQ[n_] := n >= 2 && Or @@ IntegerQ /@ Sqrt[5*n^2 + {-4, 4}]; Select[Range[300], !fibQ[Max[FactorInteger[#][[;;, 2]]] + 1] &]

PARI

isfib(n) = n >= 2 && (issquare(5*n^2-4) || issquare(5*n^2+4));
is(n) = n > 1 && !isfib(vecmax(factor(n)[,2]) + 1);