|
%I #29 Dec 16 2018 00:22:26
%S 16447,41467,41647,44617,46147,46471,76441,114451,144511,146407,
%T 404167,404671,414607,415141,416407,440761,441607,451411,460147,
%U 460417,461407,470461,476041,476401,541141,610447,640741,644107,644701,647401,704461,740461,746041,764041
%N Primes p such that sum of cubes of even digits of p equals sum of cubes of odd digits of p.
%C Minimal number of digits in p is 5. n such that sum of even digits equals sum of odd digits in A036301.
%C 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
%H Marius A. Burtea, <a href="/A076166/b076166.txt">Table of n, a(n) for n = 1..5869</a>
%e 16447 is OK because 1^3 + 7^3 = 6^3 + 4^3 + 4^3.
%e 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
%t 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 *)
%o (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
%Y Cf. A009994, A036301.
%Y Subsequence of A076165.
%K nonn,base,less
%O 1,1
%A _Zak Seidov_, Nov 01 2002
|
