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%I #20 Sep 08 2022 08:46:19
%S 3,1753,1999,2389,2713,3301,3361,3529,3583,3607,3631,3643,3697,3889,
%T 3907,4093,4099,4129,4153,4159,4243,4423,4591,4639,4813,5167,5449,
%U 5503,5527,5563,5683,5689,5827,6199,6211,6427,6529,6553,6691,6709,6883,6949,6961,6997
%N Primes p such that sum of digits of p^3 is a perfect square.
%C All the terms in this sequence, except a(1), are congruent to 1 mod 3.
%C After a(1), all the terms are congruent to {1, 4, 7} mod 9.
%H K. D. Bajpai, <a href="/A290944/b290944.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 3 is prime: 3^3 = 27; 2 + 7 = 9 = 3^2.
%e a(2) = 1753 is prime: 1753^3 = 5386984777; 5 + 3 + 8 + 6 + 9 + 8 + 4 + 7 + 7 + 7 = 64 = 8^2.
%p f:= n->add(d, d=convert(n^3, base, 10)):
%p select(t -> type(sqrt(f(t)), integer), [seq(ithprime(m), m=1..10^3)]);
%t Select[Prime[Range[2000]], IntegerQ[Sqrt[Plus @@ IntegerDigits[#^3]]] &]
%o (PARI) forprime(p=1, 5000, if(issquare(sumdigits(p^3)), print1(p, ", ")));
%o (Magma) [p: p in PrimesUpTo(1000) | IsSquare(&+Intseq(p^3))];
%o (PARI) is(n) = ispseudoprime(n) && issquare(sumdigits(n^3)) \\ _Felix Fröhlich_, Aug 14 2017
%Y Cf. A007605, A052279, A079130, A086924, A235398, A259418, A290843.
%K nonn,base
%O 1,1
%A _K. D. Bajpai_, Aug 14 2017
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