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
Examples
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.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..10000
Programs
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Magma
[p: p in PrimesUpTo(1000) | IsSquare(&+Intseq(p^3))];
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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)]);
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Mathematica
Select[Prime[Range[2000]], IntegerQ[Sqrt[Plus @@ IntegerDigits[#^3]]] &]
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PARI
forprime(p=1, 5000, if(issquare(sumdigits(p^3)), print1(p, ", ")));
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PARI
is(n) = ispseudoprime(n) && issquare(sumdigits(n^3)) \\ Felix Fröhlich, Aug 14 2017
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