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 A101681 #18 Aug 31 2024 17:45:00
%S A101681 7,16,17,19,22,25,31,34,38,42,43,45,46,47,49,52,55,58,61,64,67,70,71,
%T A101681 72,73,76,77,79,80,82,87,88,92,93,94,97,100,102,103,104,106,107,110,
%U A101681 112,115,117,122,123,124,127,129,130,133,136,139,142,143,145,147,148
%N A101681 Numbers k such that gcd(C(2k,k), 2k+1) > 1.
%C A101681 Positions where A056616 differs from A000984.
%C A101681 The set seems to have greater cardinality than its complement.
%C A101681 Positions where A055786 differs from A001790. - _Mohammed Yaseen_, Aug 03 2024
%H A101681 David A. Corneth, <a href="/A101681/b101681.txt">Table of n, a(n) for n = 1..10000</a>
%e A101681 7 is in the sequence as gcd(binomial(2*7, 7), 2*7 + 1) = gcd(3432, 15) = gcd(3*1144, 3*5) > 1. - _David A. Corneth_, Apr 03 2021
%t A101681 Select[Range[200],GCD[Binomial[2 #,#],2 #+1]>1&] (* _Harvey P. Dale_, May 11 2019 *)
%o A101681 (PARI) is(n) = { my(f = factor(2*n+1)); for(i = 1, #f~, if(val(2*n, f[i, 1])-2*val(n, f[i, 1]) > 0, return(1))); 0 }
%o A101681 val(n, p) = my(r=0); while(n, r+=n\=p); r \\ _David A. Corneth_, Apr 03 2021
%Y A101681 Cf. A000984, A056616, A126786.
%K A101681 nonn
%O A101681 1,1
%A A101681 _Ralf Stephan_, Dec 11 2004