

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

T. D. Noe, Table of n, a(n) for n = 1..1201 (terms < 10^7)
David Pagni, 82.27 An interesting number fact, The Mathematical Gazette 82:494 (1998), pp. 271273.
C. Rivera, PP&P Puzzle 158: Sum of Cubes equal to Square of Sum


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).
Cf. A227072, A227073.
Sequence in context: A237960 A023937 A068896 * A216444 A083428 A183780
Adjacent sequences: A225564 A225565 A225566 * A225568 A225569 A225570


KEYWORD

nonn,base,fini,easy


AUTHOR

Balarka Sen, Jul 26 2013


EXTENSIONS

Corrected by T. D. Noe, Jul 26 2013


STATUS

approved



