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 A231847 #36 Sep 20 2022 05:22:13 %S A231847 3,7,11,19,23,43,47,71,107,131,163,167,179,211,223,251,271,307,359, %T A231847 419,431,439,443,467,503,571,691,751,811,827,839,863,907,947,967,971, %U A231847 991,1019,1031,1063,1091,1103,1187,1279,1427,1483,1499,1559,1583,1607,1723,1759,1783 %N A231847 Primes p such that p*(p+1)/2 + 1 is a prime. %C A231847 From _Bernard Schott_, Sep 18 2022: (Start) %C A231847 A000217(p) must be even, so these primes p satisfy p == 3 (mod 4) (A002145). %C A231847 Corresponding values of A000217(p) + 1 are in A231988. %C A231847 The smallest prime of the form 4*k + 3 that is not a term is 31 because A000217(31) = 496, then 496 + 1 = 497 = 7 * 71 (see Penguin reference). (End) %D A231847 David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, London, England, 1997, entry 496, page 142. %e A231847 A000217(3) + 1 = 3*4/2 + 1 = 7, hence 3 is a term. %t A231847 Select[Prime[Range[300]], PrimeQ[# (# + 1)/2 + 1] &] (* _T. D. Noe_, Nov 19 2013 *) %o A231847 (PARI) isok(p) = isprime(p) && isprime(p*(p+1)/2+1); \\ _Michel Marcus_, Sep 19 2022 %Y A231847 Cf. A000040, A000217, A231988, A231989, A357218. %Y A231847 Subsequence of A002145. %K A231847 nonn %O A231847 1,1 %A A231847 _Alex Ratushnyak_, Nov 16 2013