A217722 Primes one less than the sum of the square of a prime and the cube of a prime.

11, 149, 173, 293, 367, 463, 631, 653, 1303, 1451, 1493, 1499, 1619, 1973, 2221, 2333, 2551, 2557, 2699, 3011, 3037, 3539, 3823, 3877, 4139, 4831, 4937, 5051, 5081, 5273, 5441, 6659, 6761, 6883, 6907, 7013, 7027, 7121, 7219, 7237, 7699, 8219, 8263, 8539, 8707

Offset

1,1

Comments

A number p is a term of this sequence iff p = q^2 + r^3 - 1 where p, q and r are all prime.

There are 1064 such numbers < 10^7.

Links

Table of n, a(n) for n=1..45.

Example

173 is in the sequence because 173 = 7^2 + 5^3 - 1, and 173, 7, and 5 are all prime.

Mathematica

max = 10^4; Take[Select[Sort[Flatten[Table[Prime[p]^2 + Prime[q]^3 - 1, {p, PrimePi[Sqrt[max]]}, {q, PrimePi[max^(1/3)]}]]], PrimeQ[#] && # < max &] (* Alonso del Arte, Mar 22 2013 *)

Crossrefs

This sequence contains the prime numbers from A045699-1;

primes of the form p1^2 + p2^3: A045700;

primes of the form p1^2 + p2^3 + 1: A217734.

Sequence in context: A194726 A367790 A296143 * A261536 A175635 A103544

Adjacent sequences: A217719 A217720 A217721 * A217723 A217724 A217725

Keyword

nonn

Author

Kevin L. Schwartz & Christian N. K. Anderson, Mar 22 2013

Status

approved