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%I #38 Sep 06 2016 11:38:22
%S 1,11,22,111,122,236,244,333,1111,1122,1236,1244,1333,2222,2488,2666,
%T 3366,3446,4444,11111,11122,11236,11244,11333,12222,12488,12666,13366,
%U 13446,14444,22236,22244,22333,26999,28888,33999,34688,36666,44488,44666,55555,111111,111122
%N Numbers n with digits in nondecreasing order such that sum of the reciprocal of digits is an integer.
%C 236 is a member and 263, 326, 362, 623, 632 which are digit permutations of 236 are not included (unlike A037268). Subsidiary sequences: (1) Sum of the reciprocals of all n-digit members. (2) Let the terms with reciprocal sum n be arranged in nondecreasing order. (i) The n-th term in the above sequence (2). (ii) The number of digits in this term of (i).
%C Subsequence of A009994. - _David A. Corneth_, Sep 05 2016
%H Harvey P. Dale and David A. Corneth, <a href="/A091784/b091784.txt">Table of n, a(n) for n = 1..10001</a> (First 237 terms from Harvey P. Dale)
%e 236 is a member as 1/2 + 1/3 +1/6 = 1.
%t Do[l = IntegerDigits[n]; If[Intersection[l, {0}] == {} && IntegerQ[Plus @@ Map[(1/#)&, l]] && Sort[l] == l, Print[n]], {n, 1, 10^5}] (* _Ryan Propper_, Aug 27 2005 *)
%t Select[Range[50000],Min[Differences[IntegerDigits[#]]]>=0&&IntegerQ[ Total[ 1/IntegerDigits[#]]]&] (* _Harvey P. Dale_, Aug 22 2016 *)
%o (PARI) is(n)=my(d=digits(n), v=vecsort(d),s); if(d==v, s=sum(i=1,#d,1/d[i]); s==s\1, 0) \\ _David A. Corneth_, Sep 06 2016
%o (PARI) getNDigitTerms(n)=my(v=List(),t); forvec(x=vector(8,i,[0,n]), my(u=vector(n,i,1),X=concat(x,n)); for(i=2,9, for(j=X[i-1]+1, X[i],u[j]=i)); if(denominator(sum(i=1,#u,1/u[i]))==1, listput(v,fromdigits(u))),1); Set(v) \\ _Charles R Greathouse IV_, Sep 06 2016
%Y Cf. A009994, A037268, A034708.
%K base,nonn
%O 1,2
%A _Amarnath Murthy_, Feb 17 2004
%E More terms from _Ryan Propper_, Aug 27 2005
%E Name corrected by _David A. Corneth_, Sep 05 2016
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