A055013 Sum of 4th powers of digits of n.

0, 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 1, 2, 17, 82, 257, 626, 1297, 2402, 4097, 6562, 16, 17, 32, 97, 272, 641, 1312, 2417, 4112, 6577, 81, 82, 97, 162, 337, 706, 1377, 2482, 4177, 6642, 256, 257, 272, 337, 512, 881, 1552, 2657, 4352, 6817

Offset: 0

Author

Henry Bottomley, May 31 2000

Keywords

• base
• nonn

Comments

Fixed points are listed in A052455, row 4 of A252648. See also A061210. - M. F. Hasler, Apr 12 2015

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• K. Chikawa, K. Iséki, and T. Kusakabe, On a problem by H. Steinhaus, Acta Arithmetica 7 (1962), 251-252. - _Don Knuth_, Sep 07 2015
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A003132, A055012.

Cf. A007953, A055017, A076313, A076314.

Cf. A052455, A252648; A061210.

Programs

Magma

[0] cat [&+[d^4: d in Intseq(n)]: n in [1..50]]; // Bruno Berselli, Feb 01 2013

Maple

A055013 := proc(n)
        add(d^4,d=convert(n,base,10)) ;
end proc:
seq(A055013(n),n=0..20) ; # R. J. Mathar, Nov 07 2011

Mathematica

Table[Sum[DigitCount[n][[i]] i^4, {i, 9}], {n, 0, 50}] (* Bruno Berselli, Feb 01 2013 *)
Table[Total[IntegerDigits[n]^4],{n,0,50}] (* Harvey P. Dale, Jul 28 2019 *)

PARI

a(n)=round(normlp(n,4)^4) \\ Quite slow. - M. F. Hasler, Apr 12 2015

PARI

A055013(n)=sum(i=1,#n=digits(n),n[i]^4) \\ M. F. Hasler, Apr 12 2015

Formula

a(n) = sum{k>0, (floor(n/10^k)-10*floor(n/10^(k+1)))^4}. - Hieronymus Fischer, Jun 25 2007

a(10n+k) = a(n)+k^4, 0<=k<10. - Hieronymus Fischer, Jun 25 2007