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 A067317 #23 Jul 18 2024 09:18:39
%S A067317 1,3,7,15,23,31,59,63,67,81,84,93,95,127,157,170,214,239,253,255,313,
%T A067317 470,511,622,694,1010,1023,1098,1691,2047,3535,3836,3963,4095,6143,
%U A067317 7166,8191,11757,12525,12686,16383,32767
%N A067317 Numbers k such that 1 + binomial(k,j) is prime for only 2 values of j (0 <= j <= k).
%F A067317 Numbers k such that A067316(k) = 2.
%e A067317 The 2 values of j are 0 and n, which give the prime 2. The sequence includes all numbers of the form 2^m-1 since binomial(2^m-1,j) is odd for all j.
%t A067317 test[n_] := Module[{}, For[i=1, 2i<=n, i++, If[PrimeQ[Binomial[n, i]+1], Return[False]]]; True]; For[n=1, True, n++, If[test[n], Print[n]]]
%o A067317 (PARI) isok(n) = sum(j=0, n, isprime(1 + binomial(n,j))) == 2; \\ _Michel Marcus_, Oct 30 2018
%o A067317 (PARI) is(n) = if(n == 1, 1, for(i=1, n\2, if(isprime(binomial(n, i) + 1), return(0))); 1); \\ _Amiram Eldar_, Jul 18 2024
%Y A067317 Cf. A067316.
%K A067317 nonn,more
%O A067317 1,2
%A A067317 _Labos Elemer_, Jan 15 2002
%E A067317 More terms from _Jon E. Schoenfield_, May 30 2010
%E A067317 a(35)-a(41) from _Robert Israel_, Mar 09 2020
%E A067317 a(42) from _Amiram Eldar_, Jul 18 2024