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

1,1

Comments

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

Links

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

Example

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.

Mathematica

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

Prog

(PARI) forprime(p=1, 10^6, if(issquare(sumdigits(p)^3 + p), print1(p, ", ")))
(Magma) [p: p in PrimesUpTo(2*10^6) |  IsSquare(&+Intseq(p)^3 + p)] ;

Crossrefs

Cf. A052034, A061309, A091365, A091366.

Sequence in context: A087191 A158959 A355052 * A253416 A275483 A125354

Adjacent sequences: A259415 A259416 A259417 * A259419 A259420 A259421

Keyword

nonn,base

Author

K. D. Bajpai, Jun 26 2015

Status

approved