A259418 Primes p such that p plus the cube of sum of digits of p is a perfect square.

17, 131, 863, 1031, 1481, 3011, 3449, 3881, 3923, 5903, 16649, 17921, 22643, 26249, 26687, 30113, 30809, 33629, 48473, 56009, 58049, 60623, 70163, 71933, 75521, 94109, 109331, 129209, 134129, 155387, 179909, 193601, 194003, 195401, 219647, 239807, 258233, 263411

Offset: 1

Author

K. D. Bajpai, Jun 26 2015

Keywords

• nonn
• base

Comments

All the terms are congruent to 2 (mod 3).

Examples

			a(2) = 131 is prime: 131 + (1 + 3 + 1)^3 = 256 = 16^2.
a(3) = 863 is prime: 863 + (8 + 6 + 3)^3 = 5776 = 76^2.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..2610

Crossrefs

Cf. A052034, A061309, A091365, A091366.

Programs

Magma

[p: p in PrimesUpTo(2*10^6) |  IsSquare(&+Intseq(p)^3 + p)] ;

Mathematica

Select[Prime[Range[100000]], IntegerQ[Sqrt[# + Plus @@ (IntegerDigits[#])^3]] &]

PARI

forprime(p=1, 10^6, if(issquare(sumdigits(p)^3 + p), print1(p, ", ")))