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 A136327 #26 Feb 12 2025 14:04:35 %S A136327 2,3,5,7,9,11,13,17,19,23,25,29,31,37,41,43,47,49,53,59,61,67,71,73, %T A136327 79,83,89,97,101,103,107,109,113,121,125,127,131,137,139,149,151,157, %U A136327 163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251 %N A136327 Numbers k > 1 such that binomial(2k-1, k-1) == 1 (mod k). %C A136327 k such that A099905(k) = 1. %C A136327 Contains primes, squares of odd primes and cubes of primes >= 5. %C A136327 See A228562 for terms that are neither primes nor prime powers. [_Joerg Arndt_, Aug 27 2013] %H A136327 Robert Israel, <a href="/A136327/b136327.txt">Table of n, a(n) for n = 1..10000</a> %H A136327 McIntosh, R. J. (1995), <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa71/aa7144.pdf">On the converse of Wolstenholme's theorem</a>, Acta Arithm., LXXI.4 (1995), 381-389. %e A136327 a(3) = 5 because binomial(9, 4) = 126 == 1 (mod 5). %p A136327 filter:= k -> binomial(2*k-1,k-1) mod k = 1: %p A136327 select(filter, [$1..1000]); # _Robert Israel_, Feb 11 2025 %t A136327 Select[Range[300], Mod[Binomial[2# - 1, # - 1], #] == 1 &] (* _Alonso del Arte_, May 11 2014 *) %o A136327 (PARI) isok(n) = (binomial(2*n-1, n-1) % n) == 1; \\ _Michel Marcus_, Aug 26 2013 %Y A136327 Cf. A099905. %K A136327 nonn %O A136327 1,1 %A A136327 _Franz Vrabec_, Mar 26 2008 %E A136327 Name corrected by _Robert Israel_, Feb 11 2025