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