A291256 Numbers n such that Sum_{k>=1} digits(k)/k = 1 where digits() are the digits of n in base 10, the least significant digit having index 1.

1, 20, 300, 2010, 4000, 50000, 100110, 102100, 200200, 300010, 302000, 400100, 600000, 7000000, 20001010, 20003000, 20101100, 20301000, 40000010, 40002000, 40100100, 40300000, 60001000, 80000000, 300000200, 300100010, 300102000, 300200100, 300400000, 320101000, 340100000

Offset

1,2

Links

Michel Marcus and Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 59 terms from Michel Marcus)

Example

20 is a term since 0/1 + 2/2 = 1.
2010 is a term since 0/1 + 1/2 + 0/3 + 2/4 = 1.

Mathematica

ndig[n_] := Sort[Sum[e[[2]] 10^(1/e[[1]] - 1), {e, #}] & /@ Select[Tally /@ (Join[ {1/n}, #] & /@ IntegerPartitions[1 - 1/n, All, 1/Range[n]]), Max[Flatten[#]] < 10 &]]; Join @@ (ndig /@ Range[20]) (* Giovanni Resta, Aug 21 2017 *)

Prog

(PARI) isok(n) = my(d = Vecrev(digits(n))); sum(k=1, #d, d[k]/k) == 1;

Crossrefs

Cf. A272036 (analog in base 2).

Sequence in context: A016255 A322052 A250014 * A250015 A344197 A138794

Adjacent sequences: A291253 A291254 A291255 * A291257 A291258 A291259

Keyword

nonn,base

Author

Michel Marcus, Aug 21 2017

Status

approved