A235398 -id:A235398 - cp's OEIS frontend

A235399 Numbers which are the digital sum of the cube of some prime.

8, 9, 10, 17, 19, 26, 28, 35, 37, 44, 46, 53, 55, 62, 64, 71, 73, 80, 82, 89, 91, 98, 100, 107, 109, 116, 118, 125, 127, 134, 136, 143, 145, 152, 154, 161, 163, 170, 172, 179, 181, 188, 190, 197, 199, 206, 208, 215, 217, 224, 226, 233, 235, 242, 244, 251, 253

Offset: 1

Antonio Graciá Llorente, Jan 09 2014

A235398 sorted and duplicates removed.

Cf. A235398, A004164, A007953, A123157.

Total[IntegerDigits[#]] & /@ (Prime[Range[5000000]]^3) // Union (* The program generates the first 39 terms of the sequence. To generate more, increase the Range constant. *) (* Harvey P. Dale, Sep 19 2021 *)

list(maxx)={v=List();n=2; while(n<=maxx,q=n^3;summ=sumdigits(q);
if(setsearch(v,summ)<1,listput(v,summ));n=nextprime(n+1));vecsort(v,,8) ;} \\ Bill McEachen, Jan 29 2014

Conjecture: for n > 4, a(n) = a(n-2) + 9 = A056020(n).

Conjecture: a(n) = (1/4)*(-1)^n*(9*(-1)^n*(2*n-1) + 5), n >= 3. - Bill McEachen, Feb 13 2021

a(37)-a(57) from Lars Blomberg, Feb 10 2016

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

Original entry on oeis.org

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

K. D. Bajpai, Aug 14 2017

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.

			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.

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

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

[p: p in PrimesUpTo(1000) | IsSquare(&+Intseq(p^3))];

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

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

forprime(p=1, 5000, if(issquare(sumdigits(p^3)), print1(p, ", ")));

is(n) = ispseudoprime(n) && issquare(sumdigits(n^3)) \\ Felix Fröhlich, Aug 14 2017

A290963 Primes p such that sum of digits of p^3 is semiprime.

Original entry on oeis.org

3, 7, 29, 41, 53, 59, 71, 83, 89, 113, 131, 137, 149, 157, 167, 173, 179, 197, 199, 227, 233, 239, 251, 263, 269, 281, 293, 317, 347, 379, 401, 409, 419, 431, 457, 463, 467, 479, 491, 503, 509, 521, 569, 617, 619, 641, 643, 647, 661, 677, 691, 701, 733, 743, 757, 761, 769, 797, 823, 829, 859, 883, 911

Offset: 1

K. D. Bajpai, Aug 15 2017

			a(2) = 7 is prime: 7^3 = 343; 3 + 4 + 3 = 10 = 2*5 that is semiprime.
a(3) = 29 is prime : 29^3 = 24389; 2 + 4 + 3 + 8 + 9 = 26 = 2*13 that is semiprime.
a(5) = 53 is prime : 53^3 = 148877; 1 + 4 + 8 + 8 + 7 + 7 = 35 = 5*7 that is semiprime.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A000040, A007605, A001358, A235398, A235399.

select(p -> isprime(p) and numtheory:-bigomega(convert(convert(p^3,base,10),`+`)) = 2, [seq(i,i=3..1000,2)]); # Robert Israel, Aug 15 2017

Select[Prime[Range[500]], PrimeOmega[Plus @@ IntegerDigits[#^3]] == 2 &]

lista(nn) = forprime(p=3, nn, if(bigomega(sumdigits(p^3)) == 2, print1(p, ", "))); \\ Altug Alkan, Aug 16 2017

A291052 Primes p such that the sum of the cubes of digits of p equals the sum of digits of p^3.

Original entry on oeis.org

2, 31, 103, 1321, 2003, 3001, 3221, 10303, 21323, 23021, 30203, 30313, 31123, 31223, 31321, 32003, 33013, 33211, 100003, 102241, 103231, 113023, 122033, 122321, 130223, 131203, 132001, 132103, 133201, 133213, 200003, 203311, 210233, 213203, 220411, 221303, 223211

Offset: 1

K. D. Bajpai, Aug 17 2017

			a(2)=31 is prime: [3^3 + 1^3 = 27 + 1] = 28; [31^3 = 29791, 2+9+7+9+1] = 28.
a(4)=1321 is prime: [1^3 + 3^3 + 2^3 + 1^3 = 1 + 27 + 8 + 1] = 37; [31^3 = 2305199161, 2+3+0+5+1+9+9+1+6+1] = 37.

Intersection of A000040 and A165551.

Cf. A000578, A030078, A235398, A290972.

Select[Prime[Range[30000]], Total[IntegerDigits[#]^3] == Plus @@ IntegerDigits[#^3] &]

forprime(p=1, 30000, d=digits(p); if(sum(i=1, length(d), d[i]^3) == sumdigits(p^3), print1(p", ")));

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A235399 Numbers which are the digital sum of the cube of some prime.

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

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A290963 Primes p such that sum of digits of p^3 is semiprime.

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Maple

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A291052 Primes p such that the sum of the cubes of digits of p equals the sum of digits of p^3.

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Examples

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Programs

Mathematica

PARI