

A225567


Primes with nonzero digits such that sum of cubes of digits equal to square of sums.


3



1423, 2143, 2341, 4231, 12253, 21523, 22153, 22531, 23251, 25321, 32251, 35221, 36343, 36433, 43633, 52321, 64333, 114451, 144511, 224461, 244261, 246241, 365557, 415141, 424261, 426421, 446221, 446461, 451411, 462421, 466441, 541141, 555637, 556537, 556573
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OFFSET

1,1


COMMENTS

Largest term of this sequence is the 20digit prime 99151111111111111111.
The Pagni article mentioned below has no bearing on this problem because it deals with the wellknown identity sum_{i=1..n} i^3 = (sum_{i=1..n} i)^2. However, the article is interesting.  T. D. Noe, Jul 26 2013
This sequence has exactly 14068465 provable primes. This result required about one hour of Mathematica on fairly fast computer having 16 GB of memory.  T. D. Noe, Jul 30 2013


LINKS



EXAMPLE

a(5) = 12253 since 1^3 + 2^3 + 2^3 + 5^3 + 3^3 = (1 + 2 + 2 + 5 + 3)^2.


MATHEMATICA

(* let tz[[i]] be numbers computed in A227073 *) Select[tz, PrimeQ] (* T. D. Noe, Jul 30 2013 *)
pQ[n_]:=Module[{idn=IntegerDigits[n]}, FreeQ[idn, 0]&&Total[idn^3] == Total[ idn]^2]; Select[Prime[Range[50000]], pQ] (* Harvey P. Dale, Sep 17 2013 *)


PROG

(PARI)forprime(n=1, 10^7, v=digits(n); if(sum(i=1, length(v), v[i]^3)==sum(i=1, length(v), v[i])^2 & setsearch(Set(v), 0)!=1, print1(n", ")))


CROSSREFS

Cf. A055012 (sum of cubes of digits), A118881 (square of sum of the digits).


KEYWORD

nonn,base,fini,easy


AUTHOR



EXTENSIONS



STATUS

approved



