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.

A102491 Numbers whose base-20 representation can be written with decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 120, 121, 122, 123, 124, 125, 126
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 12 2005

Keywords

Comments

a(n) = A118761(n) for n<=50. - Reinhard Zumkeller, May 01 2006

Links

Crossrefs

Complement of A102492; Cf. A102487, A102489, A102493. Cf. A037454, A037462, A007091.

Programs

  • Haskell
    import Data.List (unfoldr)
a102491 n = a102491_list !! (n-1)
a102491_list = filter (all (<= 9) . unfoldr
   (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 20)) [0..]
-- Reinhard Zumkeller, Jun 27 2013
  • Maple
    seq(n + (1/2)*add(20^k*floor(n/10^k), k = 1..floor(ln(n)/ln(10))), n = 1..100); # Peter Bala, Dec 01 2016
  • Mathematica
    Select[Range@ 126, Total@ Take[Most@ DigitCount[#, 20], -10] == 0 &] (* Michael De Vlieger, Apr 09 2016 *)
  • PARI
    isok(n) = (n==0) || ((d=digits(n, 20)) && (vecmax(d) < 10)); \\ Michel Marcus, Apr 09 2016
  • PARI
    a(n) = fromdigits(digits(n-1),20) \\ Ruud H.G. van Tol, Dec 08 2022
  • Python
    A102491_list = [int(str(x), 20) for x in range(10**6)] # Chai Wah Wu, Apr 09 2016

Formula

From Peter Bala, Dec 01 2016: (Start)
If n = Sum_{i = 0..m} d(i)*10^i is the decimal expansion of n then a(n+1) = Sum_{i = 0..m} d(i)*20^i.
a(n+1) = n + 1/2*Sum_{k >= 1} 20^k*floor(n/10^k). Cf. A037454, A037462 and A007091.
a(1) = 0; a(n+1) = 20*a(n/10+1) if n == 0 (mod 10) else a(n+1) = a(n) + 1. (End)
G.f. g(x) satisfies g(x) = 20*Sum_{1<=k<=9} x^k*g(x^10)/x^9 + Sum_{1<=k<=9} k*x^(k+1)/(1-x^10). - Robert Israel, Dec 01 2016

A102490 Numbers in base-16 representation that cannot be written with decimal digits.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 26, 27, 28, 29, 30, 31, 42, 43, 44, 45, 46, 47, 58, 59, 60, 61, 62, 63, 74, 75, 76, 77, 78, 79, 90, 91, 92, 93, 94, 95, 106, 107, 108, 109, 110, 111, 122, 123, 124, 125, 126, 127, 138, 139, 140, 141, 142, 143, 154, 155, 156, 157, 158, 159, 160
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 12 2005

Keywords

Examples

			42 = 2*16^1 + 10*16^0 = '2A', therefore 42 is a term.

Links

Crossrefs

Complement of A102489; A102488, A102492, A102494.

Programs

  • Haskell
    import Data.List (unfoldr)
a102490 n = a102490_list !! (n-1)
a102490_list = filter (any (> 9) . unfoldr
   (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 16)) [0..]
-- Reinhard Zumkeller, Jun 27 2013
  • Mathematica
    Select[Range[200],IntegerLength[Max[IntegerDigits[#,16]]]>1&] (* Harvey P. Dale, Jun 12 2020 *)
  • Python
    def ok(n): return any(hd > '9' for hd in hex(n)[2:])
print(list(filter(ok, range(161)))) # Michael S. Branicky, Oct 11 2021

A102488 Numbers in base-12 representation that cannot be written with decimal digits.

Original entry on oeis.org

10, 11, 22, 23, 34, 35, 46, 47, 58, 59, 70, 71, 82, 83, 94, 95, 106, 107, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 154, 155, 166, 167, 178, 179, 190, 191, 202, 203, 214
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 12 2005

Keywords

Examples

			143 = 11*12^1 + 11*12^0 = 'BB', therefore 143 is a term.

Links

Crossrefs

Complement of A102487; A102490, A102492, A102494.

Programs

  • Haskell
    import Data.List (unfoldr)
a102488 n = a102488_list !! (n-1)
a102488_list = filter (any (> 9) . unfoldr (\x ->
   if x == 0 then Nothing else Just $ swap $ divMod x 12)) [1..]
-- Reinhard Zumkeller, Apr 18 2011
  • Mathematica
    Select[Range[250],Max[IntegerDigits[#,12]]>9&] (* Harvey P. Dale, Oct 20 2020 *)

A102494 Numbers in base-60 representation that cannot be written with decimal digits.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 12 2005

Keywords

Examples

			200 = 3*60^1 + 20*60^0 = '3K', therefore 200 is a term.

References

  • Mohammad K. Azarian, Meftah al-hesab: A Summary, MJMS, Vol. 12, No. 2, Spring 2000, pp. 75-95. Mathematical Reviews, MR 1 764 526. Zentralblatt MATH, Zbl 1036.01002.
  • Mohammad K. Azarian, A Summary of Mathematical Works of Ghiyath ud-din Jamshid Kashani, Journal of Recreational Mathematics, Vol. 29(1), pp. 32-42, 1998.

Links

Crossrefs

Complement of A102493; A102488, A102490, A102492.

Programs

  • Haskell
    import Data.List (unfoldr)
a102494 n = a102494_list !! (n-1)
a102494_list = filter (any (> 9) . unfoldr
   (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 60)) [0..]
-- Reinhard Zumkeller, Jun 27 2013
  • Mathematica
    Select[Range[100],Max[IntegerDigits[#,60]]>9&] (* Harvey P. Dale, Dec 27 2012 *)
Showing 1-4 of 4 results.

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