A214959 Numbers for which the sum of reciprocals of nonzero digits = 1.

1, 10, 22, 100, 202, 220, 236, 244, 263, 326, 333, 362, 424, 442, 623, 632, 1000, 2002, 2020, 2036, 2044, 2063, 2200, 2306, 2360, 2404, 2440, 2488, 2603, 2630, 2666, 2848, 2884, 3026, 3033, 3062, 3206, 3260, 3303, 3330, 3366, 3446, 3464, 3602, 3620, 3636

Offset: 1

Author

Reinhard Zumkeller, Aug 02 2012

Keywords

• nonn
• base

Comments

Intersection of A214957 and A214958: A214949(a(n))*A214950(a(n)) = 1.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A037268 (subsequence).

Programs

Haskell

import Data.Ratio ((%), numerator, denominator)
a214959 n = a214959_list !! (n-1)
a214959_list = [x | x <- [0..], f x 0] where
   f 0 v = numerator v == 1 && denominator v == 1
   f u v | d > 0     = f u' (v + 1 % d)
         | otherwise = f u' v  where (u',d) = divMod u 10

Magma

SumReciprocalsDigits:=func; [n: n in [1..3636] | IsOne(SumReciprocalsDigits(n))]; // Bruno Berselli, Aug 02 2012

Mathematica

idnQ[n_]:=Total[1/Select[IntegerDigits[n],#>0&]]==1; Select[Range[ 4000],idnQ] (* Harvey P. Dale, Dec 08 2012 *)