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A290944 Primes p such that sum of digits of p^3 is a perfect square. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A258720 A262652 A262500 * A116994 A172940 A096730

Adjacent sequences:  A290941 A290942 A290943 * A290945 A290946 A290947

KEYWORD

nonn,base

AUTHOR

K. D. Bajpai, Aug 14 2017

STATUS

approved

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Last modified October 24 00:04 EDT 2018. Contains 316541 sequences. (Running on oeis4.)