A231847 Primes p such that p*(p+1)/2 + 1 is a prime.

3, 7, 11, 19, 23, 43, 47, 71, 107, 131, 163, 167, 179, 211, 223, 251, 271, 307, 359, 419, 431, 439, 443, 467, 503, 571, 691, 751, 811, 827, 839, 863, 907, 947, 967, 971, 991, 1019, 1031, 1063, 1091, 1103, 1187, 1279, 1427, 1483, 1499, 1559, 1583, 1607, 1723, 1759, 1783

Offset: 1

Author

Alex Ratushnyak, Nov 16 2013

Keywords

• nonn

Comments

From Bernard Schott, Sep 18 2022: (Start)

A000217(p) must be even, so these primes p satisfy p == 3 (mod 4) (A002145).

Corresponding values of A000217(p) + 1 are in A231988.

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)

Examples

			A000217(3) + 1 = 3*4/2 + 1 = 7, hence 3 is a term.
		

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, London, England, 1997, entry 496, page 142.

Crossrefs

Cf. A000040, A000217, A231988, A231989, A357218.

Subsequence of A002145.

Programs

Mathematica

Select[Prime[Range[300]], PrimeQ[# (# + 1)/2 + 1] &] (* T. D. Noe, Nov 19 2013 *)

PARI

isok(p) = isprime(p) && isprime(p*(p+1)/2+1); \\ Michel Marcus, Sep 19 2022