A055014 Sum of 5th powers of digits of n.

0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 1, 2, 33, 244, 1025, 3126, 7777, 16808, 32769, 59050, 32, 33, 64, 275, 1056, 3157, 7808, 16839, 32800, 59081, 243, 244, 275, 486, 1267, 3368, 8019, 17050, 33011, 59292, 1024, 1025, 1056, 1267, 2048

Offset

0,3

Comments

Fixed points are listed in A052464. - M. F. Hasler, Apr 12 2015

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

K. Chikawa, K. Iséki, T. Kusakabe, and K. Shibamura, Computation of cyclic parts of Steinhaus problem for power 5, Acta Arithmetica 7 (1962), 253-254. [From Don Knuth, Sep 07 2015]

Index entries for Colombian or self numbers and related sequences

Formula

a(n) = Sum_{k>=1} (floor(n/10^k) - 10*floor(n/10^(k+1)))^5. - Hieronymus Fischer, Jun 25 2007

a(10n+k) = a(n) + k^5, 0 <= k < 10. - Hieronymus Fischer, Jun 25 2007

Maple

A055014 := proc(n)
   add(d^5, d=convert(n, base, 10)) ;
end proc: # R. J. Mathar, Jul 08 2012

Mathematica

Total/@(IntegerDigits[Range[50]]^5)  (* Harvey P. Dale, Jan 22 2011 *)
Table[Sum[DigitCount[n][[i]] i^5, {i, 9}], {n, 0, 45}] (* Bruno Berselli, Feb 01 2013 *)

Prog

(Magma) [0] cat [&+[d^5: d in Intseq(n)]: n in [1..45]]; // Bruno Berselli, Feb 01 2013
(PARI) A055014(n)=sum(i=1, #n=digits(n), n[i]^5) \\ M. F. Hasler, Apr 12 2015

Crossrefs

Cf. A003132, A055012, A055013.

Cf. A007953, A055017, A076313, A076314.

Cf. A052464.

Sequence in context: A017674 A184979 A257855 * A000584 A352051 A050752

Adjacent sequences: A055011 A055012 A055013 * A055015 A055016 A055017

Keyword

base,nonn

Author

Henry Bottomley, May 31 2000

Status

approved