A302649 Numbers that are the sum of some fixed power of the digits of their ten's complement.

5, 8, 14, 3953, 33626, 89843301, 71341793655800, 245916794707565, 19429639306542698, 36106092555634673, 1818632037625982420, 4099389352522800257, 51096092690519702666, 1361788669288181208317, 80939622935362328928524, 3061856409269150191916609

Offset: 1

Author

Paolo P. Lava, Apr 11 2018

Keywords

• nonn
• base

Comments

No other term up to 3*10^12. - Giovanni Resta, Apr 12 2018

Examples

			(10 - 5) = 5 and 5^1 = 5;
(10 - 8) = 2 and 2^3 = 8;
(100 - 14) = 86 and 8^1 + 6^1 = 14;
(10000 - 3953) = 6047 and 6^4 + 0^4 + 4^4 + 7^4 = 3953;
(100000 - 33626) = 66374 and 6^5 + 6^5 + 3^5 + 7^5 + 4^5 = 33626;
(100000000 - 89843301) = 10156699 and 1^8 + 0^8 + 1^8 + 5^8 + 6^8 + 6^8 + 9^8 + 9^8 = 89843301.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..22

Crossrefs

Cf. A023052, A261433, A302651.

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);

Extensions

a(7)-a(16) from Chai Wah Wu, Jun 06 2018