A037264 Numbers whose sum of reciprocals of digits is the reciprocal of an integer.

1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 36, 44, 63, 66, 88, 236, 244, 263, 326, 333, 362, 424, 442, 488, 623, 632, 666, 848, 884, 999, 2488, 2666, 2848, 2884, 3366, 3446, 3464, 3636, 3644, 3663, 4288, 4346, 4364, 4436, 4444, 4463, 4634, 4643, 4828, 4882, 6266, 6336

Offset

1,2

Comments

Intersection of A214958 and A052382: A214949(a(n))*A168046(a(n)) = 1. - Reinhard Zumkeller, Aug 02 2012

Links

T. D. Noe, Table of n, a(n) for n = 1..1232 (complete sequence)

Example

63 is a term: 1/((1/6) + (1/3)) = 2.

Mathematica

Reap[Do[If[FreeQ[id = IntegerDigits[n], 0], If[IntegerQ[1/Total[1/id]], Sow[n]]], {n, 1, 10^4}]][[2, 1]] (* Jean-François Alcover, Dec 15 2015 *)
Select[Range[6500], FreeQ[IntegerDigits[#], 0]&&IntegerQ[1/Total[1/IntegerDigits[#]]]&] (* Harvey P. Dale, Sep 29 2024 *)

Prog

(Haskell)
a037264 n = a037264_list !! (n-1)
a037264_list = filter ((== 1) . a168046) $
                      takeWhile (<= 999999999) a214958_list
-- Reinhard Zumkeller, Aug 02 2012
(PARI) isok(n) = {my(d=digits(n)); vecmin(d) && (numerator(sum(k=1, #d, 1/d[k])) == 1); } \\ Michel Marcus, May 24 2018
(Python)
from fractions import Fraction
def ok(n):
    ds = list(map(int, str(n)))
    return 0 not in ds and sum(Fraction(1, d) for d in ds).numerator == 1
print(list(filter(ok, range(1, 6337)))) # Michael S. Branicky, Aug 08 2021

Crossrefs

Cf. A037265, A045910.

Sequence in context: A083158 A254956 A061013 * A274124 A045910 A128290

Adjacent sequences: A037261 A037262 A037263 * A037265 A037266 A037267

Keyword

easy,nonn,nice,base,fini,full

Author

Naohiro Nomoto

Status

approved