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A259418
Primes p such that p plus the cube of sum of digits of p is a perfect square.
2
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
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
KEYWORD
nonn,base
AUTHOR
K. D. Bajpai, Jun 26 2015
STATUS
approved