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A055013 Sum of 4th powers of digits of n.

%I A055013 #32 Sep 08 2022 08:45:01
%S A055013 0,1,16,81,256,625,1296,2401,4096,6561,1,2,17,82,257,626,1297,2402,
%T A055013 4097,6562,16,17,32,97,272,641,1312,2417,4112,6577,81,82,97,162,337,
%U A055013 706,1377,2482,4177,6642,256,257,272,337,512,881,1552,2657,4352,6817
%N A055013 Sum of 4th powers of digits of n.
%C A055013 Fixed points are listed in A052455, row 4 of A252648. See also A061210. - _M. F. Hasler_, Apr 12 2015
%H A055013 Seiichi Manyama, <a href="/A055013/b055013.txt">Table of n, a(n) for n = 0..10000</a>
%H A055013 K. Chikawa, K. Iséki, and T. Kusakabe, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa7/aa733.pdf">On a problem by H. Steinhaus</a>, Acta Arithmetica 7 (1962), 251-252. - _Don Knuth_, Sep 07 2015
%H A055013 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%F A055013 a(n) = sum{k>0, (floor(n/10^k)-10*floor(n/10^(k+1)))^4}. - _Hieronymus Fischer_, Jun 25 2007
%F A055013 a(10n+k) = a(n)+k^4, 0<=k<10. - _Hieronymus Fischer_, Jun 25 2007
%p A055013 A055013 := proc(n)
%p A055013         add(d^4,d=convert(n,base,10)) ;
%p A055013 end proc:
%p A055013 seq(A055013(n),n=0..20) ; # _R. J. Mathar_, Nov 07 2011
%t A055013 Table[Sum[DigitCount[n][[i]] i^4, {i, 9}], {n, 0, 50}] (* _Bruno Berselli_, Feb 01 2013 *)
%t A055013 Table[Total[IntegerDigits[n]^4],{n,0,50}] (* _Harvey P. Dale_, Jul 28 2019 *)
%o A055013 (Magma) [0] cat [&+[d^4: d in Intseq(n)]: n in [1..50]]; // _Bruno Berselli_, Feb 01 2013
%o A055013 (PARI) a(n)=round(normlp(n,4)^4) \\ Quite slow. - _M. F. Hasler_, Apr 12 2015
%o A055013 (PARI) A055013(n)=sum(i=1,#n=digits(n),n[i]^4) \\ _M. F. Hasler_, Apr 12 2015
%Y A055013 Cf. A003132, A055012.
%Y A055013 Cf. A007953, A055017, A076313, A076314.
%Y A055013 Cf. A052455, A252648; A061210.
%K A055013 base,nonn
%O A055013 0,3
%A A055013 _Henry Bottomley_, May 31 2000