login
A286126
Numbers k such that k = Sum_{i=1..j} Sd(k)^i, for some j>0, where Sd(k) is the sum of the digits of k.
0
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 42, 90, 100, 120, 156, 1000, 3615, 5219, 6174, 9723, 10000, 18278, 22620, 47988, 54240, 100000, 551880, 837930, 1000000, 2000718, 10000000, 12204240, 12356630, 25137930, 40358373, 54066635, 62193780, 100000000, 133878822, 168751484
OFFSET
1,2
COMMENTS
Any power of 10 (A011557) is a term of the sequence.
Subsequence of A005349.
EXAMPLE
The sum of the digits of 22620 is 2 + 2 + 6 + 2 + 0 = 12 and 12 + 12^2 + 12^3 + 12^4 = 22620.
MAPLE
S:=proc(w) local x; x:=add(x, x=convert(w, base, 10)); end:
P:= proc(q) local a, k, n; for n from 1 to q do a:=S(n); k:=1;
while a<n do k:=k+1; a:=a+S(n)^k; od; if a=n then print(n); fi; od; end: P(10^8);
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, May 03 2017
STATUS
approved