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 1-7 of 7 results.

A120000 Record values in A119999.

Original entry on oeis.org

1, 2, 8, 12, 298, 1230, 10494, 74543, 238174, 402385, 608924, 858896, 1150972, 1486709, 1864309, 2285798, 91850628, 4005374676, 4028841935, 69750785781, 88657850823, 95628273398, 154486668208, 3487100060522, 49842735693373, 263064249410400, 751941667877632, 1790364658467926, 3748860728854527
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 13 2006

Keywords

Comments

a(n)=A119999(A120001(n)) and A119999(m)A120001(n).

Examples

			21 is where a record occurs in A119999 and A119999(21) = 12 so 12 is a record value of A119999. - _David A. Corneth_, Sep 07 2022

Links

Extensions

Corrected by T. D. Noe, Oct 25 2006
More terms from David A. Corneth, Sep 07 2022

A120001 Where record values of A119999 occur.

Original entry on oeis.org

0, 10, 12, 21, 102, 112, 123, 213, 312, 412, 512, 612, 712, 812, 912, 1012, 1023, 1123, 1213, 1234, 1324, 1423, 2113, 2134, 3124, 4123, 5123, 6123, 7123, 8123, 9123, 10123, 10234, 11213, 11234, 12134, 12345, 13245, 14235, 15234, 16234, 17234, 18234, 19234, 21134, 21345
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 13 2006

Keywords

Comments

A120000(n)=A119999(a(n)) and A119999(m) < A120000(n) for m
problem: smallest m>1023456789 such that A119999(m)>A119999(1023456789)?
From David A. Corneth, Sep 07 2022: (Start)
Does every term >= 10 contain the digit 1?
Does every term >= 12 contain the digits 1 and 2?
Does every term >= 1023 contain the digits 1, 2 and 3?
Does every term >= 11234 contain the digits 1, 2, 3 and 4?
Does every term >= 112345 contain the digits 1, 2, 3, 4 and 5? (End)

Examples

			21 is in the sequence as A119999(21) = 12 and 12 is the largest value of A119999(k) for k in [0, 21]. - _David A. Corneth_, Sep 07 2022

Links

Crossrefs

Cf. A001399, A001400, A004526, A119999, A120000.

Extensions

More terms from David A. Corneth, Sep 07 2022

A120002 First differences of A119999.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 6, -2, -1, 0, -1, 0, 0, 0, -2, 10, -10, 3, 3, -4, 2, -3, 2, -2, -1, 10, -5, -5, 2, 0, 4, -5, 0, 3, -4, 10, 0, -7, -3, 2, 1, -2, 5, -5, -1, 10, -5, -2, -1, -2, 1, 0, 0, 0, -1, 10, 0, 0, -5, -3, -2, 1, 1, 1, -3, 10, -5, -2, -1, 0, -1, -1, 1, 0, -1, 10, 0, -7, 7, -8, 1, -2, -1, 1, -1, 10, -5, 5, -8, 0, 3, -4
Offset: 0

Views

Author

Reinhard Zumkeller, Jun 13 2006

Keywords

Comments

a(n) = A119999(n+1) - A119999(n).

Crossrefs

Cf. A120003.

Extensions

Corrected by N. J. A. Sloane, Oct 01 2006

A120003 Partial sums of A119999.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 22, 28, 33, 38, 42, 46, 50, 54, 56, 68, 70, 75, 83, 87, 93, 96, 101, 104, 106, 118, 125, 127, 131, 135, 143, 146, 149, 155, 157, 169, 181, 186, 188, 192, 197, 200, 208, 211, 213, 225, 232, 237, 241, 243, 246, 249, 252, 255, 257
Offset: 0

Views

Author

Reinhard Zumkeller, Jun 13 2006

Keywords

Comments

a(0) = A119999(0), a(n) = a(n-1) + A119999(n).

Crossrefs

Cf. A120002.

A061827 Number of partitions of n into parts which are the digits of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 5, 4, 4, 3, 3, 3, 3, 1, 11, 1, 4, 7, 3, 5, 2, 4, 2, 1, 11, 6, 1, 3, 3, 7, 2, 2, 5, 1, 11, 11, 4, 1, 3, 4, 2, 7, 2, 1, 11, 6, 4, 3, 1, 2, 2, 2, 2, 1, 11, 11, 11, 6, 3, 1, 2, 3, 4, 1, 11, 6, 4, 3, 3, 2, 1, 2, 2, 1, 11, 11, 4, 11, 3, 4, 2, 1, 2, 1, 11, 6, 11, 3, 3, 6, 2, 2
Offset: 1

Views

Author

Amarnath Murthy, May 28 2001

Keywords

Comments

a(A125289(n)) = 1, a(A125290(n)) > 1.

Examples

			For n = 11, 1+1+1+1+1+1+1+1+1+1+1. so a(11) = 1. For n = 12, 2+2+2+2+2+2 = 2+2+1+1+1+1+1+1+1+1 = ...etc
a(20) = 1: the only partitions permitted use the digits 0 and 2, so there is just 1, 20 = 2+2+2... ten times.

Links

Crossrefs

Cf. A061828, A109950, A119999, A125291, A136460, A193513.

Programs

  • Haskell
    import Data.List (sort, nub)
import Data.Char (digitToInt)
a061827 n =
   p n (map digitToInt $ nub $ sort $ filter (/= '0') $ show n) where
      p _ []        = 0
      p 0 _         = 1
      p m ds'@(d:ds)
        | m < d     = 0
        | otherwise = p (m - d) ds' + p m ds
-- Reinhard Zumkeller, Aug 01 2011
  • Mathematica
    Length[IntegerPartitions[#,All,DeleteDuplicates@DeleteCases[IntegerDigits[#],0]]]&/@Range[200] (* Sander G. Huisman, Nov 14 2022 *)

Extensions

More terms from David Wasserman, Jul 29 2002

A120004 Number of distinct numbers as substrings of n in decimal representation.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 4, 4, 5, 5, 5, 5
Offset: 0

Views

Author

Reinhard Zumkeller, Jun 15 2006

Keywords

Comments

a(n) = A079790(n) for n <= 100;
a(A120005(n)) = n and a(m) < n for m < A120005(n).
a(n) = length of n-th row in A218978; see also A154771. - Reinhard Zumkeller, Nov 10 2012

Examples

			n=101: {'1','0','10','01','101'} -> a(101) = #{0,1,10,101} = 4;
n=102: {'1','0','2','10','02','102'} -> a(102) = #{0,1,2,10,102} = 5.

Links

Crossrefs

Cf. A119999.

Programs

  • Haskell
    import Data.List (isInfixOf)
a120004 n = sum $ map (fromEnum . (`isInfixOf` show n) . show) [0..n]
-- Reinhard Zumkeller, Jul 16 2012, Aug 14 2011
  • Mathematica
    a[n_] := Length@ DeleteDuplicates[FromDigits /@ Rest@ Subsequences[ IntegerDigits[n]]]; Array[a, 100, 0] (* Amiram Eldar, Oct 19 2021 *)
  • PARI
    a(n) = if (n==0, return (1)); my(d=digits(n), list=List()); for (k=1, #d, for (j=1, #d-k+1, my(dk=vector(j, i, d[k+i-1])); listput(list, fromdigits(dk)););); #Set(list); \\
  • Python
    def A120004(n):
    s = str(n)
    m = len(s)
    return len(set(int(s[i:j]) for i in range(m) for j in range(i+1,m+1))) # Chai Wah Wu, Oct 19 2021

Extensions

Offset changed and a(0)=1 inserted, in consequence of Zak Seidov's correction in A120005. - Reinhard Zumkeller, May 30 2010

A193513 Number of partitions of n into parts having at least one common digit in decimal representation.

Original entry on oeis.org

1, 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 3, 8, 5, 9, 9, 13, 9, 16, 12, 18, 16, 23, 20, 31, 30, 38, 38, 51, 49, 64, 62, 79, 77, 95, 101, 118, 118, 143, 145, 179, 181, 216, 223, 267, 286, 325, 341, 399, 416, 485, 500, 575, 600, 686, 735, 823, 864, 981, 1032, 1180
Offset: 0

Views

Author

Reinhard Zumkeller, Jul 30 2011

Keywords

Examples

			a(7) = #{7, 7x1} = 2;
a(8) = #{8, 4+4, 2+2+2+2, 8x1} = 4;
a(9) = #{9, 3+3+3, 9x1} = 3;
a(10) = #{10, 5+5, 2+2+2+2+2, 10x1} = 4;
a(11) = #{11, 10+1, 11x1} = 3;
a(12) = #{12, 11+1, 10+1+1, 6+6, 4+4+4, 3+3+3+3, 6x2, 10x1} = 8;
a(13) = #{13, 12+1, 11+1+1, 10+1+1+1, 13x1} = 5;
a(14) = #{14, 13+1, 12+2, 12+1+1, 11+1+1+1, 10+4x1, 7+7, 7x2, 14x1} = 9.

Crossrefs

Cf. A061827, A061828, A109950, A119999.

Programs

  • Haskell
    import Data.List (intersect)
a193513 n = p "0123456789" n 1 where
   p ""        = 0
   p   0       = 1
   p cds m k
     | m < k     = 0
     | otherwise = p (cds `intersect` show k) (m - k) k + p cds m (k + 1)

Extensions

Thanks to Douglas McNeil, who noticed a program error; data corrected and program fixed by Reinhard Zumkeller, Aug 01 2011
Showing 1-7 of 7 results.

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

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