A107408 Form the sum of the digits of a(n); a(n+1) is the smallest unused integer having a copy of every digit of this sum.

0, 10, 1, 11, 2, 12, 3, 13, 4, 14, 5, 15, 6, 16, 7, 17, 8, 18, 9, 19, 100, 21, 23, 25, 27, 29, 101, 20, 22, 24, 26, 28, 102, 30, 31, 34, 37, 103, 40, 41, 35, 38, 110, 32, 45, 39, 112, 42, 36, 49, 113, 50, 51, 46, 104, 52, 47, 111, 33, 56, 114, 60, 61, 57, 120, 43, 67, 123, 62

Offset

0,2

Comments

The "seed" is 0 in this case.

This is a permutation of the nonnegative integers. - Nadia Heninger, Aug 10 2005

Links

R. J. Mathar, Feb 21 2008, Table of n, a(n) for n = 0..93

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

Example

Sum of the digits of 29 is 11; the smallest available integer which has a copy of every digit of 11 is 101 (not 31).

Maple

A007953 := proc(n) add(i, i=convert(n, base, 10)) ; end: multDigs := proc(n) local a, dgs, i; if n = 0 then a := [1, seq(0, i=1..9)] ; else a := [seq(0, i=0..9)] ; dgs := convert(n, base, 10) ; for i in dgs do a := subsop(i+1=op(i+1, a)+1, a) ; od: fi ; RETURN(a) ; end: A107408 := proc(nmax) local a, ds, dsk, k, works, d ; a := [0] ; while nops(a) < nmax do ds := multDigs(A007953(op(-1, a))) ; for k from 1 do if not k in a then dsk := multDigs(k) ; works := true; for d from 1 to 10 do if op(d, dsk) < op(d, ds) then works := false ; break ; fi ; od: if works then a := [op(a), k] ; break ; fi ; fi ; od: od: RETURN(a) ; end: A107408(120) ; # R. J. Mathar, Feb 21 2008

Crossrefs

Sequence in context: A332177 A130858 A098760 * A129888 A239113 A107353

Adjacent sequences: A107405 A107406 A107407 * A107409 A107410 A107411

Keyword

base,easy,nonn

Author

Eric Angelini, Jun 09 2005

Extensions

Corrected and extended by R. J. Mathar, Feb 21 2008

Status

approved