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.

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.

Links

Table of n, a(n) for n=1..41.

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

Cf. A005349, A007953, A011557.

Sequence in context: A048335 A068862 A061729 * A249157 A033621 A332808

Adjacent sequences: A286123 A286124 A286125 * A286127 A286128 A286129

Keyword

nonn,base

Author

Paolo P. Lava, May 03 2017

Status

approved