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Numbers that are the sum of some fixed power of the digits of their ten's complement.
2

%I #15 Jun 25 2018 02:57:21

%S 5,8,14,3953,33626,89843301,71341793655800,245916794707565,

%T 19429639306542698,36106092555634673,1818632037625982420,

%U 4099389352522800257,51096092690519702666,1361788669288181208317,80939622935362328928524,3061856409269150191916609

%N Numbers that are the sum of some fixed power of the digits of their ten's complement.

%C No other term up to 3*10^12. - _Giovanni Resta_, Apr 12 2018

%H Chai Wah Wu, <a href="/A302649/b302649.txt">Table of n, a(n) for n = 1..22</a>

%e (10 - 5) = 5 and 5^1 = 5;

%e (10 - 8) = 2 and 2^3 = 8;

%e (100 - 14) = 86 and 8^1 + 6^1 = 14;

%e (10000 - 3953) = 6047 and 6^4 + 0^4 + 4^4 + 7^4 = 3953;

%e (100000 - 33626) = 66374 and 6^5 + 6^5 + 3^5 + 7^5 + 4^5 = 33626;

%e (100000000 - 89843301) = 10156699 and 1^8 + 0^8 + 1^8 + 5^8 + 6^8 + 6^8 + 9^8 + 9^8 = 89843301.

%p with(numtheory): P:=proc(q) local a,b,i,j,k,n;

%p for n from 1 to q do a:=convert(10^(ilog10(n)+1)-n,base,10);

%p b:=convert(a,`+`); j:=1; i:=0; while n>b do

%p if i=b then break; else i:=b; j:=j+1; b:=add(a[k]^j,k=1..nops(a)); fi; od;

%p if n=b then print(n); fi; od; end: P(10^9);

%Y Cf. A023052, A261433, A302651.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Apr 11 2018

%E a(7)-a(16) from _Chai Wah Wu_, Jun 06 2018