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 1-5 of 5 results.

A037265 Integers arising from A037264.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 2, 2, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

Keywords

Comments

The remaining terms are all 1.

Crossrefs

Cf. A037264.

Extensions

More terms from Erich Friedman.

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

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

Crossrefs

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

A214949 Numerator of sum of reciprocals of all nonzero digits of n in decimal representation.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 3, 1, 5, 3, 7, 2, 9, 5, 11, 1, 4, 5, 2, 7, 8, 1, 10, 11, 4, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 1, 6, 7, 8, 9, 2, 11, 12, 13, 14, 1, 7, 2, 1, 5, 11, 1, 13, 7, 5, 1, 8, 9, 10, 11, 12, 13, 2, 15, 16
Offset: 0

Views

Author

Reinhard Zumkeller, Aug 02 2012

Keywords

Crossrefs

Cf. A214950 (denominators).

Programs

  • Haskell
    import Data.Ratio ((%), numerator)
    a214949 = f 0 where
       f y 0 = numerator y
       f y x = f (y + if d == 0 then 0 else 1 % d) x'
               where (x',d) = divMod x 10
    
  • Mathematica
    nsr[n_] := Numerator[Total[1/Select[IntegerDigits[n], # > 0 &]]]; nsr /@ Range[0, 79] (* Jayanta Basu, Jul 13 2013 *)
  • PARI
    a(n) = my(d=digits(n)); numerator(sum(k=1, #d, if (d[k], 1/d[k]))); \\ Michel Marcus, Jan 26 2022

Formula

a(A037264(n)) = a(A037268(n)) = a(A214958(n)) = a(A214959(n)) = 1;
a(n) = a(A004719(n)).

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.

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

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 1-5 of 5 results.