A225793 - OEIS

A225793

Numbers n that can be uniquely expressed as (m + sum of digits of m) for some m.

2, 4, 6, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Subset of A176995; first member in A176995 that is not here is 101, next is 103 (cf. A230094).

A230093(a(n)) = 1. - Reinhard Zumkeller, Oct 11 2013

REFERENCES

Joshi, V. S. A note on self-numbers. Volume dedicated to the memory of V. Ramaswami Aiyar. Math. Student 39 (1971), 327--328 (1972). MR0330032 (48 #8371)

Makowski, Andrzej. On Kaprekar's "junction numbers''. Math. Student 34 1966 77 (1967). MR0223292 (36 #6340)

Narasinga Rao, A. On a technique for obtaining numbers with a multiplicity of generators. Math. Student 34 1966 79--84 (1967). MR0229573 (37 #5147)

LINKS

Jayanta Basu and Donovan Johnson, Table of n, a(n) for n = 1..10000 (first 1000 terms from Jayanta Basu)

Index entries for Colombian or self numbers and related sequences

EXAMPLE

100 is a member as 100 = 86 + sum of digits of (86). 101 is not a member since both 91 and 100 generate 101. Again 103 is not a member as 92 and 101 generate 103.

MAPLE

For Maple code see A230093. - N. J. A. Sloane, Oct 11 2013

MATHEMATICA

co[n_] := Count[Range[n - 1], _?(# + Total[IntegerDigits[#]] == n &)]; Select[Range[100], co[#] == 1 &]

Select[Tally[Table[m+Total[IntegerDigits[m]], {m, 100}]], #[[2]]==1&][[All, 1]]// Sort (* Harvey P. Dale, Aug 23 2017 *)

PROG

(Haskell)

a225793 n = a225793_list !! (n-1)

a225793_list = filter ((== 1) . a230093) [1..]

-- Reinhard Zumkeller, Oct 11 2013

CROSSREFS

Cf. A007953, A062028, A004207, A230093, A003052, A176995, A230094.