A231847 - OEIS

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

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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.