A357218 Primes p such that T(p) - 2 is prime, where T(p) is the triangular number (A000217) with index p.

5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 149, 157, 193, 197, 233, 257, 269, 277, 281, 313, 337, 389, 401, 409, 457, 509, 521, 541, 613, 641, 673, 701, 797, 857, 877, 881, 929, 953, 997, 1009, 1033, 1093, 1109, 1117, 1129, 1153, 1193, 1297, 1301, 1373, 1381, 1433, 1481, 1493

Offset

1,1

Comments

T(p) must be odd, so these primes p satisfy p == 1 (mod 4) (A002144).

Corresponding values of T(p)-2 are in A357219.

The first eleven primes == 1 (mod 4) are terms. The smallest Pythagorean prime that is not a term is A002144(12) = 101 because T(101) = 5151 and 5151 - 2 = 5149 = 19 * 271 (see Wells reference).

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..55.

Example

T(5) - 2 = 5*6/2 - 2 = 13, hence 5 is a term.

Maple

filter := p -> isprime(p) and irem(p-1, 4) = 0 and isprime(p*(p+1)/2 -2) : select(filter, [$1 .. 1500]);

Mathematica

Select[Prime[Range[240]], PrimeQ[#*(# + 1)/2 - 2] &] (* Amiram Eldar, Sep 18 2022 *)

Crossrefs

Cf. A000217, A231847, A357219.

Subsequence of A002144.

Sequence in context: A280084 A319287 A192592 * A349900 A347163 A111055

Adjacent sequences: A357215 A357216 A357217 * A357219 A357220 A357221

Keyword

nonn

Author

Bernard Schott, Sep 18 2022

Status

approved