A076166 Primes p such that sum of cubes of even digits of p equals sum of cubes of odd digits of p.

16447, 41467, 41647, 44617, 46147, 46471, 76441, 114451, 144511, 146407, 404167, 404671, 414607, 415141, 416407, 440761, 441607, 451411, 460147, 460417, 461407, 470461, 476041, 476401, 541141, 610447, 640741, 644107, 644701, 647401, 704461, 740461, 746041, 764041

Offset

1,1

Comments

Minimal number of digits in p is 5. n such that sum of even digits equals sum of odd digits in A036301.

To find terms of this sequence, one could look at zerofree positive integers having the criterion on sum of cubes of digits. Then permute the digits to see which are prime. Using those digits with 0 and permuting then only needs the check on primality. - David A. Corneth, Dec 11 2018

Links

Marius A. Burtea, Table of n, a(n) for n = 1..5869

Example

16447 is OK because 1^3 + 7^3 = 6^3 + 4^3 + 4^3.
14467 has digits in nondecreasing order (is zerofree). Of the 60 permutations, 16447, 41467, 41647, 44617, 46147, 46471, 76441 are prime. - David A. Corneth, Dec 11 2018

Mathematica

oeQ[n_]:=Module[{idn = IntegerDigits[n]}, Total[Select[idn, OddQ]^3] == Total[ Select[idn, EvenQ]^3]]; Select[Range[100000], PrimeQ[#] && oeQ[#] &] (* Amiram Eldar, Dec 10 2018 after Harvey P. Dale at A076165 *)

Prog

(PARI) isok(p) = isprime(p) && (d=digits(p)) && (sum(i=1, #d, d[i]^3*if(d[i]%2, 1, -1))==0); \\ Michel Marcus, Dec 13 2018

Crossrefs

Cf. A009994, A036301.

Subsequence of A076165.

Sequence in context: A122714 A133533 A250844 * A168665 A283027 A031829

Adjacent sequences: A076163 A076164 A076165 * A076167 A076168 A076169

Keyword

nonn,base,less

Author

Zak Seidov, Nov 01 2002

Status

approved