A302651 Numbers that are the product of some fixed power of the digits of their ten's complement.
5, 8, 81, 2016, 2205
Offset: 1
Examples
(10 - 5) = 5 and 5^1 = 5; (10 - 8) = 2 and 2^3 = 8; (100 - 81) = 19 and 1^2 * 9^2 = 81; (10000 - 2016) = 7984 and 7^1 * 9^1 * 8^1 * 4^1 = 2016; (10000 - 2205) = 7795 and 7^1 * 7^1 * 9^1 * 5^1 = 2205;
Programs
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Maple
with(numtheory): P:=proc(q) local a,b,i,j,k,n; for n from 1 to q do a:=convert(10^(ilog10(n)+1)-n,base,10); b:=convert(a,`*`); j:=1; i:=0; while n>b do if i=b then break; else i:=b; j:=j+1; b:=add(a[k]^j,k=1..nops(a)); fi; od; if n=b then print(n); fi; od; end: P(10^9);
Comments