cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A037268 Sum of reciprocals of digits = 1.

Original entry on oeis.org

1, 22, 236, 244, 263, 326, 333, 362, 424, 442, 623, 632, 2488, 2666, 2848, 2884, 3366, 3446, 3464, 3636, 3644, 3663, 4288, 4346, 4364, 4436, 4444, 4463, 4634, 4643, 4828, 4882, 6266, 6336, 6344, 6363, 6434, 6443, 6626, 6633, 6662, 8248, 8284, 8428, 8482, 8824
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

This sequence has 1209 terms.
Intersection of A037264 and A034708: A214949(a(n))*A214950(a(n))*A168046(a(n)) = 1. - Reinhard Zumkeller, Aug 02 2012

Links

Crossrefs

Cf. A020473, A037264, A038034.
Subsequence of A214959.

Programs

  • Haskell
    a037268 n = a037268_list !! (n-1)
a037268_list = filter ((== 1) . a168046) $
                      takeWhile (<= 999999999) a214959_list
-- Reinhard Zumkeller, Aug 02 2012
  • Maple
    A037268 := proc(n) option remember: local d,k: if(n=1)then return 1: fi: for k from procname(n-1)+1 do d:=convert(k,base,10): if(not member(0,d) and add(1/d[j],j=1..nops(d))=1)then return k: fi: od: end: seq(A037268(n),n=1..50); # Nathaniel Johnston, May 28 2011
  • Mathematica
    Select[Range[10000],Total[1/(IntegerDigits[#]/.(0->1))]==1&] (* Harvey P. Dale, Jul 23 2025 *)
  • PARI
    lista(nn) = {for (n=1, nn, d = digits(n); if (vecmin(d) && (sum(k=1, #d, 1/d[k])==1), print1(n, ", ")););} \\ Michel Marcus, Jul 06 2015
  • Python
    from fractions import Fraction
def ok(n):
  sn = str(n)
  return False if '0' in sn else sum(Fraction(1, int(d)) for d in sn) == 1
def aupto(limit): return [m for m in range(1, limit+1) if ok(m)]
print(aupto(8824)) # Michael S. Branicky, Jan 22 2021

Extensions

More terms from Christian G. Bower, Jun 15 1998
Two missing terms inserted by Nathaniel Johnston, May 28 2011

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

Original entry on oeis.org

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

Views

Author

Naohiro Nomoto

Keywords

Comments

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

Examples

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

Links

Crossrefs

Cf. A037265, A045910.

Programs

  • Haskell
    a037264 n = a037264_list !! (n-1)
a037264_list = filter ((== 1) . a168046) $
                      takeWhile (<= 999999999) a214958_list
-- Reinhard Zumkeller, Aug 02 2012
  • 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 *)
  • 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

A214950 Denominator of sum of reciprocals of all nonzero digits of n in decimal representation.

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 2, 1, 6, 4, 10, 3, 14, 8, 18, 3, 3, 6, 3, 12, 15, 2, 21, 24, 9, 4, 4, 4, 12, 2, 20, 12, 28, 8, 36, 5, 5, 10, 15, 20, 5, 30, 35, 40, 45, 6, 6, 3, 2, 12, 30, 3, 42, 24, 18, 7, 7, 14, 21, 28, 35, 42
Offset: 0

Views

Author

Reinhard Zumkeller, Aug 02 2012

Keywords

Links

Crossrefs

Cf. A034708, A037268, A214957, A214959, A004719.
Cf. A214949 (numerators).

Programs

  • Haskell
    import Data.Ratio ((%), denominator)
a214950 = f 0 where
   f y 0 = denominator y
   f y x = f (y + if d == 0 then 0 else 1 % d) x'
           where (x',d) = divMod x 10
  • Mathematica
    dsr[n_] := Denominator[Total[1/Select[IntegerDigits[n], # > 0 &]]]; dsr /@ Range[0, 76] (* Jayanta Basu, Jul 13 2013 *)
  • PARI
    a(n) = my(d=digits(n)); denominator(sum(k=1, #d, if (d[k], 1/d[k]))); \\ Michel Marcus, Jan 26 2022

Formula

a(A034708(n)) = a(A037268(n)) = a(A214957(n)) = a(A214959(n)) = 1;
a(n) = a(A004719(n)).

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

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Aug 02 2012

Keywords

Comments

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

Links

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 *)

A214958 Numbers for which the sum of reciprocals of nonzero digits is reciprocal of an integer.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 22, 30, 36, 40, 44, 50, 60, 63, 66, 70, 80, 88, 90, 100, 200, 202, 220, 236, 244, 263, 300, 306, 326, 333, 360, 362, 400, 404, 424, 440, 442, 488, 500, 600, 603, 606, 623, 630, 632, 660, 666, 700, 800, 808, 848, 880, 884
Offset: 1

Views

Author

Reinhard Zumkeller, Aug 02 2012

Keywords

Comments

A214949(a(n)) = 1.

Links

Crossrefs

Cf. A037264 (subsequence).

Programs

  • Haskell
    a214958 n = a214958_list !! (n-1)
a214958_list = [x | x <- [0..], a214949 x == 1]
  • Mathematica
    nsrQ[n_] := Numerator[Total[1/Select[IntegerDigits[n], # > 0 &]]] == 1; Select[Range[884], nsrQ] (* Jayanta Basu, Jul 13 2013 *)

A045910 Numbers with digits nondecreasing and their reciprocals sum to 1/(positive integer).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 36, 44, 66, 88, 236, 244, 333, 488, 666, 999, 2488, 2666, 3366, 3446, 4444, 6999, 8888, 26999, 28888, 33999, 34688, 36666, 44488, 44666, 55555, 366999, 368888, 446999, 448888, 466688, 666666, 3999999, 4688999, 4888888, 6666999, 6668888, 7777777, 66999999, 68888999, 88888888, 999999999
Offset: 1

Views

Author

Len Smiley

Keywords

Comments

Intersection of A037264 and A009994, A214949(a(n)) = 1. - Reinhard Zumkeller, Aug 02 2012

Examples

			1/3 + 1/4 + 1/6 + 1/8 + 1/8 = 1/1, so 34688 is in the sequence.

Crossrefs

Condensation (by ordering digits) and completion of A037264.

Programs

  • Haskell
    a045910 n = a045910_list !! (n-1)
a045910_list =  [x | x <- takeWhile (<= 999999999) $ a009994_list,
                     a214949 x == 1]
-- Reinhard Zumkeller, Aug 02 2012
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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