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A091784
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Numbers n with digits in nondecreasing order such that sum of the reciprocal of digits is an integer.
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2
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1, 11, 22, 111, 122, 236, 244, 333, 1111, 1122, 1236, 1244, 1333, 2222, 2488, 2666, 3366, 3446, 4444, 11111, 11122, 11236, 11244, 11333, 12222, 12488, 12666, 13366, 13446, 14444, 22236, 22244, 22333, 26999, 28888, 33999, 34688, 36666, 44488, 44666, 55555, 111111, 111122
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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EXAMPLE
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236 is a member as 1/2 + 1/3 +1/6 = 1.
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MATHEMATICA
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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 *)
Select[Range[50000], Min[Differences[IntegerDigits[#]]]>=0&&IntegerQ[ Total[ 1/IntegerDigits[#]]]&] (* Harvey P. Dale, Aug 22 2016 *)
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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