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A091784 Numbers n with digits in nondecreasing order such that sum of the reciprocal of digits is an integer. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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).
Subsequence of A009994. - David A. Corneth, Sep 05 2016
LINKS
Harvey P. Dale and David A. Corneth, Table of n, a(n) for n = 1..10001 (First 237 terms from Harvey P. Dale)
EXAMPLE
236 is a member as 1/2 + 1/3 +1/6 = 1.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A081930 A143964 A034708 * A213972 A061852 A083511
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Feb 17 2004
EXTENSIONS
More terms from Ryan Propper, Aug 27 2005
Name corrected by David A. Corneth, Sep 05 2016
STATUS
approved

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Last modified May 21 21:53 EDT 2024. Contains 372738 sequences. (Running on oeis4.)