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

Author

Paolo P. Lava, Apr 11 2018

Keywords

• nonn
• base
• more

Comments

No other terms up to 10^40. - Giovanni Resta Apr 12 2018

No other terms up to 10^51 - Chai Wah Wu, Jun 06 2018

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;
		

Crossrefs

Cf. A023052, A261433, A302649.

Programs

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);