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A290944
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Primes p such that sum of digits of p^3 is a perfect square.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MAPLE
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f:= n->add(d, d=convert(n^3, base, 10)):
select(t -> type(sqrt(f(t)), integer), [seq(ithprime(m), m=1..10^3)]);
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MATHEMATICA
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Select[Prime[Range[2000]], IntegerQ[Sqrt[Plus @@ IntegerDigits[#^3]]] &]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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