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 A053663 #28 Sep 08 2022 08:45:00 %S A053663 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, %T A053663 31,32,34,35,36,37,38,40,41,42,43,44,45,46,47,48,49,50,52,53,54,55,56, %U A053663 57,58,59,60,61,62,64,66,67,68,69,70,71,72,73,74,75 %N A053663 Numbers k such that 2*k+1 does not divide k!+1. %H A053663 G. C. Greubel, <a href="/A053663/b053663.txt">Table of n, a(n) for n = 1..10000</a> %t A053663 Select[Range[100],!Divisible[#!+1,2#+1]&] (* _Harvey P. Dale_, Sep 09 2014 *) %o A053663 (PARI) isok(n) = (n!+1) % (2*n+1) \\ _Michel Marcus_, Jul 12 2013 %o A053663 (Magma) [n: n in [1..100] | not (Factorial(n)+1) mod (2*n+1) eq 0 ]; // _G. C. Greubel_, May 18 2019 %o A053663 (Sage) [n for n in (1..100) if not Mod(factorial(n)+1, 2*n+1)==0 ] # _G. C. Greubel_, May 18 2019 %o A053663 (GAP) Filtered([1..100], n-> not (Factorial(n)+1) mod (2*n+1)=0) # _G. C. Greubel_, May 18 2019 %Y A053663 Cf. A005097, complement of A053662. %K A053663 easy,nonn %O A053663 1,2 %A A053663 _Chris K. Caldwell_, Feb 16 2000 %E A053663 Data corrected by _Michel Marcus_, Jul 12 2013