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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Largest term of this sequence is the 20-digit prime 99151111111111111111.

The Pagni article mentioned below has no bearing on this problem because it deals with the well-known 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. 271-273.

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

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Last modified August 5 17:20 EDT 2021. Contains 346488 sequences. (Running on oeis4.)