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 1-4 of 4 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

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

Links

Crossrefs

Cf. A004719, A037264, A037268, A214958, A214959.
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)).

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)).

A239685 Prime numbers for which the sum of reciprocals of nonzero digits equals 1.

Original entry on oeis.org

263, 2063, 4463, 4643, 6203, 20063, 26003, 60443, 62003, 64403, 68483, 69929, 86843, 88463, 88643, 92699, 200063, 260003, 260999, 296099, 296909, 400643, 406403, 406883, 446003, 449699, 460403, 464003, 464999, 468803, 488603, 494699, 496499, 496949, 499649
Offset: 1

Views

Author

Michel Lagneau, Mar 24 2014

Keywords

Comments

Primes in A214959.
Property of the sequence: a(n) == 3 or 9 (mod 10). If n contains nonzero digits, each number > 263 contains at least two identical digits, and the subsequence of the corresponding sum of reciprocals of digits (primes in A037268) is finite.

Examples

			2063 is in the sequence because 1/2 + 1/6 + 1/3 = 1.

Crossrefs

Cf. A037268, A214959.

Programs

  • Maple
    with(numtheory):nn:=500000:for m from 1 to nn do:n:=ithprime(m):y:=convert(n,base,10):n2:=nops(y):s:=0:for i from 1 to n2 do: if y[i]<>0 then s:=s+1/y[i]:else fi:od:if s=1 then printf(`%d, `,n):else fi:od:
  • Mathematica
    Select[Prime[Range[42000]],Total[1/Select[IntegerDigits[#],#!=0&]]==1&] (* Harvey P. Dale, May 31 2019 *)
Showing 1-4 of 4 results.

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

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