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 A067775 #43 Feb 16 2025 08:32:45
%S A067775 2,5,11,17,23,29,31,41,47,53,59,61,71,73,83,89,101,107,113,131,137,
%T A067775 139,149,151,157,167,173,179,181,191,197,199,211,227,233,239,241,251,
%U A067775 257,263,269,271,281,283,293,311,317,331,337,347,353,359,367,373,383,389
%N A067775 Primes p such that p + 4 is composite.
%C A067775 Primes n such that n!*B(n+3) is an integer where B(k) are the Bernoulli numbers B(1) = -1/2, B(2) = 1/6, B(4) = -1/30, ..., B(2m+1) = 0 for m > 1.
%C A067775 If n is prime n!*B(n-1) is always an integer. Note that if Goldbach's conjecture (2n = p1 + p2 for all n >= 2) is false and K is the smallest value of n for which it fails, then for 2(K-2) = p3 + p4, the primes p3 and p4 must be taken from this list. See similar comment for A140555. - _Keith Backman_, Apr 06 2012
%C A067775 Complement of A023200 (primes p such that p + 4 is also prime) with respect to A000040 (primes). For p > 2: primes p such that there is no prime of the form r^2 + p where r is prime, subsequence of A232010. Example: the prime 7 is not in the sequence because 2^2 + 7 = 11 (prime). A232009(a(n)) = 0 for n > 1 . - _Jaroslav Krizek_, Nov 22 2013
%H A067775 Klaus Brockhaus, <a href="/A067775/b067775.txt">Table of n, a(n) for n = 1..1026</a>
%H A067775 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BernoulliNumber.html">Bernoulli Number</a>
%F A067775 a(n) ~ n log n. - _Charles R Greathouse IV_, Nov 22 2013
%t A067775 A067775 = {}; Do[p = Prime@ n; If[ IntegerQ[ p! BernoulliB[p + 3]], AppendTo[A067775, p]], {n, 77}]; A067775 (* _Robert G. Wilson v_, Aug 19 2008 *)
%t A067775 Select[Prime[Range[80]], Not[PrimeQ[# + 4]] &] (* _Alonso del Arte_, Apr 02 2014 *)
%o A067775 (PARI) lista(nn) = {forprime(p=1, nn, if (! isprime(p+4), print1(p, ", ")););} \\ _Michel Marcus_, Nov 22 2013
%Y A067775 Cf. A049591, A140555, A232009, A232010, A232012, A023200.
%K A067775 nonn
%O A067775 1,1
%A A067775 _Benoit Cloitre_, Feb 06 2002
%E A067775 New name from _Klaus Brockhaus_ at the suggestion of _Michel Marcus_, Nov 22 2013