A053663 Numbers k such that 2*k+1 does not divide k!+1.

1, 2, 4, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75

Offset: 1

Author

Chris K. Caldwell, Feb 16 2000

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005097, complement of A053662.

Programs

GAP

Filtered([1..100], n-> not (Factorial(n)+1) mod (2*n+1)=0) # G. C. Greubel, May 18 2019

Magma

[n: n in [1..100] | not (Factorial(n)+1) mod (2*n+1) eq 0 ]; // G. C. Greubel, May 18 2019

Mathematica

Select[Range[100],!Divisible[#!+1,2#+1]&] (* Harvey P. Dale, Sep 09 2014 *)

PARI

isok(n) = (n!+1) % (2*n+1) \\ Michel Marcus, Jul 12 2013

Sage

[n for n in (1..100) if not Mod(factorial(n)+1, 2*n+1)==0 ] # G. C. Greubel, May 18 2019

Extensions

Data corrected by Michel Marcus, Jul 12 2013