A290944 Primes p such that sum of digits of p^3 is a perfect square.

3, 1753, 1999, 2389, 2713, 3301, 3361, 3529, 3583, 3607, 3631, 3643, 3697, 3889, 3907, 4093, 4099, 4129, 4153, 4159, 4243, 4423, 4591, 4639, 4813, 5167, 5449, 5503, 5527, 5563, 5683, 5689, 5827, 6199, 6211, 6427, 6529, 6553, 6691, 6709, 6883, 6949, 6961, 6997

Offset

1,1

Comments

All the terms in this sequence, except a(1), are congruent to 1 mod 3.

After a(1), all the terms are congruent to {1, 4, 7} mod 9.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

a(1) = 3 is prime: 3^3 = 27; 2 + 7 = 9 = 3^2.
a(2) = 1753 is prime: 1753^3 = 5386984777; 5 + 3 + 8 + 6 + 9 + 8 + 4 + 7 + 7 + 7 = 64 = 8^2.

Maple

f:= n->add(d, d=convert(n^3, base, 10)):
select(t -> type(sqrt(f(t)), integer), [seq(ithprime(m), m=1..10^3)]);

Mathematica

Select[Prime[Range[2000]], IntegerQ[Sqrt[Plus @@ IntegerDigits[#^3]]] &]

Prog

(PARI) forprime(p=1, 5000, if(issquare(sumdigits(p^3)), print1(p, ", ")));
(Magma) [p: p in PrimesUpTo(1000) | IsSquare(&+Intseq(p^3))];
(PARI) is(n) = ispseudoprime(n) && issquare(sumdigits(n^3)) \\ Felix Fröhlich, Aug 14 2017

Crossrefs

Cf. A007605, A052279, A079130, A086924, A235398, A259418, A290843.

Sequence in context: A397319 A262652 A262500 * A116994 A367542 A172940

Adjacent sequences: A290941 A290942 A290943 * A290945 A290946 A290947

Keyword

nonn,base

Author

K. D. Bajpai, Aug 14 2017

Status

approved