A091784 Numbers n with digits in nondecreasing order such that sum of the reciprocal of digits is an integer.

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

Offset: 1

Author

Amarnath Murthy, Feb 17 2004

Keywords

• base
• nonn

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

Examples

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

Links

• Harvey P. Dale and David A. Corneth, Table of n, a(n) for n = 1..10001 (First 237 terms from Harvey P. Dale)

Crossrefs

Cf. A009994, A037268, A034708.

Programs

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 *)

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

Extensions

More terms from Ryan Propper, Aug 27 2005

Name corrected by David A. Corneth, Sep 05 2016