A091783 Numbers with digits in nondecreasing order such that sum of the reciprocals of the digits is 1.

1, 22, 236, 244, 333, 2488, 2666, 3366, 3446, 4444, 26999, 28888, 33999, 34688, 36666, 44488, 44666, 55555, 366999, 368888, 446999, 448888, 466688, 666666, 3999999, 4688999, 4888888, 6666999, 6668888, 7777777, 66999999, 68888999, 88888888, 999999999

Offset: 1

Author

Amarnath Murthy, Feb 17 2004

Keywords

• base
• fini
• nonn
• full

Comments

236 is a member but 263, 326, 362, 623, 632 which are digit permutations of 236 are not included (unlike A037268).

By definition, this is a subsequence of A052382 (zeroless numbers). - Michel Marcus, Jul 06 2015

Examples

			236 is a member as 1/2 + 1/3 + 1/6 = 1.
		

Crossrefs

Cf. A037268, A052382.

Programs

Maple

F:= proc(t,ns) option remember;
   local n0, k,r;
   if ns = [] then
      if t = 0 then return {[]}
      else return {}
      fi;
   fi;
   n0:= ns[1];
   `union`(seq(map(r -> [k,op(r)], procname(t - k/n0, ns[2..-1])),k=0..floor(t*n0)));
end proc:
g:= proc(t) local L,i; L:= [seq(i$t[i],i=1..9)]; add(L[i]*10^(nops(L)-i),i=1..nops(L)) end proc:
sort(convert(map(g,F(1,[$1..9])),list)); # Robert Israel, Jul 06 2015

PARI

lista(nn) = {for (n=1, nn, d = digits(n); if (vecmin(d) && (vecsort(d)==d) && (sum(k=1, #d, 1/d[k])==1), print1(n, ", ")););} \\ Michel Marcus, Jul 06 2015

Extensions

More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Apr 17 2004

Incorrect term 39999 corrected to 33999 by Thomas Oléron Evans, Jul 06 2015