A226767 Let an integer with k+1 digits as n = d(k)*10^k + d(k-1)*10^(k-1) + ... + d(0)*10^0 and consider the transform T(n) = k*10^d(k) + (k-1)*10^d(k-1) + ... + 0*10^d(0). a(n) gives the fixed points of the transform T(n).

0, 10, 120, 201, 210, 1032, 1230, 2301, 2310, 3003, 3012, 3120, 3201, 3210, 10045, 10243, 12340, 13042, 13240, 20404, 20413, 21430, 23401, 23410, 34003, 34012, 34120, 34201, 34210, 40006, 40015, 40123, 40204, 40213, 41032, 41230, 42301, 42310, 43003, 43012

Offset

0,2

Comments

At least one digit of T(n) must be zero otherwise the unitary digit of n is lost.

Links

Paolo P. Lava, Table of n, a(n) for n = 0..1000

Formula

n = Sum_{j=0..k} j*10^d(j).

Example

For n=10045 the transform gives T(10045) = 4*10^1 + 3*10^0+ 2*10^0 + 1*10^4 + 0*10^5 = 40 + 3 + 2 + 10000 + 0 = 10045.

Maple

with(numtheory); ListA226767:=proc(q) local a, b, k, n;
for n from 0 to q do a:=trunc(n/10); b:=0; k:=0;
while a>0 do k:=k+1; b:=b+k*10^(a mod 10); a:=trunc(a/10); od;
if b=n then print(n); fi; od; end: ListA226767(10^6);

Crossrefs

Sequence in context: A030022 A069673 A069498 * A307620 A300522 A252874

Adjacent sequences: A226764 A226765 A226766 * A226768 A226769 A226770

Keyword

nonn,easy,base

Author

Paolo P. Lava, Jun 17 2013

Status

approved