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%I #11 Jun 06 2018 23:08:25
%S 5,8,81,2016,2205
%N Numbers that are the product of some fixed power of the digits of their ten's complement.
%C No other terms up to 10^40. - _Giovanni Resta_ Apr 12 2018
%C No other terms up to 10^51 - _Chai Wah Wu_, Jun 06 2018
%e (10 - 5) = 5 and 5^1 = 5;
%e (10 - 8) = 2 and 2^3 = 8;
%e (100 - 81) = 19 and 1^2 * 9^2 = 81;
%e (10000 - 2016) = 7984 and 7^1 * 9^1 * 8^1 * 4^1 = 2016;
%e (10000 - 2205) = 7795 and 7^1 * 7^1 * 9^1 * 5^1 = 2205;
%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, A302649.
%K nonn,base,more
%O 1,1
%A _Paolo P. Lava_, Apr 11 2018
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