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

1,1

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)

References

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

Links

Table of n, a(n) for n=1..53.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Subsequence of A002145.

Sequence in context: A191037 A292083 A135932 * A105876 A354801 A141101

Adjacent sequences: A231844 A231845 A231846 * A231848 A231849 A231850

Keyword

nonn

Author

Alex Ratushnyak, Nov 16 2013

Status

approved