A225793 - OEIS

%I #35 Aug 23 2017 16:26:18

%S 2,4,6,8,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,

%T 32,33,34,35,36,37,38,39,40,41,43,44,45,46,47,48,49,50,51,52,54,55,56,

%U 57,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,76,77

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

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

%C A230093(a(n)) = 1. - _Reinhard Zumkeller_, Oct 11 2013

%D 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)

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

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

%H Jayanta Basu and Donovan Johnson, <a href="/A225793/b225793.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Jayanta Basu)

%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>

%e 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.

%p For Maple code see A230093. - _N. J. A. Sloane_, Oct 11 2013

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

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

%o (Haskell)

%o a225793 n = a225793_list !! (n-1)

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

%o -- _Reinhard Zumkeller_, Oct 11 2013

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

%K nonn,base

%O 1,1

%A _Jayanta Basu_, Jul 27 2013