A357218 -id:A357218 - cp's OEIS frontend

A357219 Primes of the form T(p) - 2 where T(p) is the triangular number (A000217) with prime index p in A357218.

13, 89, 151, 433, 701, 859, 1429, 1889, 2699, 4003, 4751, 11173, 12401, 18719, 19501, 27259, 33151, 36313, 38501, 39619, 49139, 56951, 75853, 80599, 83843, 104651, 129793, 135979, 146609, 188189, 205759, 226799, 246049, 318001, 367651, 385001, 388519, 431983, 454579

Offset: 1

Bernard Schott, Sep 18 2022

nonn

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

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000217, A357218.

Subsequence of A124199.

f:= n -> n*(n+1)/2-2:
select(isprime, map(f, [seq(ithprime(i),i=1..200)])); # Robert Israel, Sep 20 2022

Select[(#*(# + 1)/2 - 2) & /@ Prime[Range[165]], PrimeQ] (* Amiram Eldar, Sep 18 2022 *)

isok(p) = my(q); isprime(p) && ispolygonal(p+2, 3, &q) && isprime(q); \\ Michel Marcus, Sep 19 2022

a(n) = A000217(A357218(n))-2.

More terms from David A. Corneth, Sep 18 2022

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

Original entry on oeis.org

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

Alex Ratushnyak, Nov 16 2013

nonn

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)

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

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

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

Subsequence of A002145.

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

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

cp's OEIS Frontend

A357219 Primes of the form T(p) - 2 where T(p) is the triangular number (A000217) with prime index p in A357218.

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