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 1-10 of 36 results. Next

A030332 Position of n-th 0 in A003137.

Original entry on oeis.org

4, 10, 16, 17, 19, 22, 26, 35, 43, 44, 46, 49, 53, 62, 70, 71, 72, 74, 75, 78, 79, 82, 84, 86, 90, 94, 96, 98, 102, 107, 108, 111, 115, 120, 132, 143, 144, 147, 151, 156, 168, 178, 179, 180, 182, 183, 186, 187, 190, 192, 194, 198, 202
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

A003137(a(n)) = 0. - Reinhard Zumkeller, Feb 21 2013

Links

Crossrefs

Cf. A030333, A030334, A030336.

Programs

  • Haskell
    import Data.List (elemIndices)
a030332 n = a030332_list !! (n-1)
a030332_list = map (+ 1) $ elemIndices 0 a003137_list
-- Reinhard Zumkeller, Feb 21 2013

A030333 Position of n-th 1 in A003137.

Original entry on oeis.org

1, 3, 5, 6, 7, 12, 15, 18, 20, 21, 24, 25, 27, 28, 29, 30, 31, 33, 36, 38, 39, 47, 52, 55, 56, 58, 65, 69, 73, 76, 77, 81, 83, 85, 87, 88, 89, 91, 93, 97, 100, 101, 105, 106, 109, 110, 112, 113, 114, 117, 118, 119, 121, 122, 123, 124, 125
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

A003137(a(n)) = 1. - Reinhard Zumkeller, Feb 21 2013

Links

Crossrefs

Cf. A030332, A030334, A030337.

Programs

  • Haskell
    import Data.List (elemIndices)
a030333 n = a030333_list !! (n-1)
a030333_list = map (+ 1) $ elemIndices 1 a003137_list
-- Reinhard Zumkeller, Feb 21 2013

A030334 Position of n-th 2 in A003137.

Original entry on oeis.org

2, 8, 9, 11, 13, 14, 23, 32, 34, 37, 40, 41, 42, 45, 48, 50, 51, 54, 57, 59, 60, 61, 63, 64, 66, 67, 68, 80, 92, 95, 99, 103, 104, 116, 128, 131, 135, 139, 140, 142, 146, 150, 152, 154, 158, 162, 164, 166, 167, 170, 171, 174, 175, 176
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

A003137(a(n)) = 2. - Reinhard Zumkeller, Feb 21 2013

Links

Crossrefs

Cf. A030332, A030333, A030338.

Programs

  • Haskell
    import Data.List (elemIndices)
a030334 n = a030334_list !! (n-1)
a030334_list = map (+ 1) $ elemIndices 2 a003137_list
-- Reinhard Zumkeller, Feb 21 2013

A030336 Length of n-th run of digit 0 in A003137.

Original entry on oeis.org

1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 3, 3, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A030337, A030338, A030332.

Programs

  • Haskell
    import Data.List (group)
a030336 n = a030336_list !! (n-1)
a030336_list = map length $ filter ((== 0) . head) $ group a003137_list
-- Reinhard Zumkeller, Feb 21 2013

A030337 Length of n-th run of digit 1 in A003137.

Original entry on oeis.org

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

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A030336, A030338, A030333.

Programs

  • Haskell
    import Data.List (group)
a030337 n = a030337_list !! (n-1)
a030337_list = map length $ filter ((== 1) . head) $ group a003137_list
-- Reinhard Zumkeller, Feb 21 2013

A030338 Length of n-th run of digit 2 in A003137.

Original entry on oeis.org

1, 2, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 3, 2, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 4, 2, 2, 3, 2, 2, 4, 3, 4, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A003137.
Cf. A030336, A030337, A030334.

Programs

  • Haskell
    import Data.List (group)
a030338 n = a030338_list !! (n-1)
a030338_list = map length $ filter ((== 2) . head) $ group a003137_list
-- Reinhard Zumkeller, Feb 21 2013

A030339 (# 1's)-(# 0's) in first n terms of A003137.

Original entry on oeis.org

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

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A003137, A030340.

Programs

  • Haskell
    a030339 n = a030339_list !! (n-1)
a030339_list = scanl1
   (\u v -> u + fromEnum (v == 1) - fromEnum (v == 0)) a003137_list
-- Reinhard Zumkeller, Feb 21 2013

A030340 a(n)=(# 1's)-(# 2's) in first n terms of A003137.

Original entry on oeis.org

1, 0, 1, 1, 2, 3, 4, 3, 2, 2, 1, 2, 1, 0, 1, 1, 1, 2, 2, 3, 4, 4, 3, 4, 5, 5, 6, 7, 8, 9, 10, 9, 10, 9, 9, 10, 9, 10, 11, 10, 9, 8, 8, 8, 7, 7, 8, 7, 7, 6, 5, 6, 6, 5, 6, 7, 6, 7, 6, 5, 4, 4, 3, 2, 3, 2, 1, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 3, 4, 4, 5, 5
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

This sequence is nonnegative: in any group of numbers with the same number of digits, the number with a 1 in a particular position always occurs before the number with a 2 in that position. In fact, 0's only occur on the last digits of (3^N)-1, where N is an integer, not the sequence index - Larry Reeves (larryr(AT)acm.org), Sep 25 2000

Links

Crossrefs

Cf. A030339.

Programs

  • Haskell
    a030340 n = a030340_list !! (n-1)
a030340_list = scanl1
   (\u v -> u + fromEnum (v == 1) - fromEnum (v == 2)) a003137_list
-- Reinhard Zumkeller, Feb 21 2013

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Sep 25 2000
Some data corrected by Reinhard Zumkeller, Feb 21 2013

A030335 a(n)=least k such that base 3 representation of n begins as s(k), where s=A003137.

Original entry on oeis.org

1, 2, 3, 5, 1, 9, 2, 8, 15, 3, 21, 20, 5, 6, 33, 1, 7, 42, 34, 9, 2, 23, 11, 8, 13, 40, 69, 15, 77, 81, 3, 89, 93, 21, 101, 76, 24, 20, 87, 27, 5, 129, 30, 6, 141, 33, 47, 1, 36, 31, 7, 12, 39, 177, 142, 42, 95, 131, 34, 201, 9, 48, 14, 2, 51, 23
Offset: 1

Views

Author

Clark Kimberling

Keywords

A007089 Numbers in base 3.

Original entry on oeis.org

0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1100, 1101, 1102, 1110, 1111, 1112, 1120, 1121, 1122, 1200, 1201, 1202, 1210, 1211
Offset: 0

Views

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

Comments

Nonnegative integers with no decimal digit > 2. Thus nonnegative integers in base 10 whose quadrupling by normal addition or multiplication requires no carry operation. - Rick L. Shepherd, Jun 25 2009

References

  • Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, ยง2.3 Positional Notation, p. 47.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A000042, A007088, A007090, A007091, A007092, A007093, A007094, A007095, A077267, A062756, A081603, A081604, A054635, A003137.
Primes when read as if in base 10: A036954.

Programs

  • Haskell
    a007089 0 = 0
a007089 n = 10 * a007089 n' + m where (n', m) = divMod n 3
-- Reinhard Zumkeller, Feb 19 2012
  • Maple
    A007089 := proc(n) option remember;
if n <= 0 then 0
else
  if (n mod 3) = 0 then 10*procname(n/3) else procname(n-1) + 1 fi
fi end:
[seq(A007089(n), n=0..729)]; # - N. J. A. Sloane, Mar 09 2019
  • Mathematica
    Table[ FromDigits[ IntegerDigits[n, 3]], {n, 0, 50}]
  • PARI
    a(n)=if(n<1,0,if(n%3,a(n-1)+1,10*a(n/3)))
  • PARI
    a(n)=fromdigits(digits(n,3)) \\ Charles R Greathouse IV, Jan 08 2017
  • Python
    def A007089(n):
  n,s = divmod(n,3); t = 1
  while n: n,r = divmod(n,3); t *= 10; s += r*t
  return s # M. F. Hasler, Feb 15 2023

Formula

a(0)=0, a(n) = 10*a(n/3) if n==0 (mod 3), a(n) = a(n-1) + 1 otherwise. - Benoit Cloitre, Dec 22 2002
a(n) = 10*a(floor(n/3)) + (n mod 3) if n > 0, a(0) = 0. - M. F. Hasler, Feb 15 2023

Extensions

More terms from James Sellers, May 01 2000
Showing 1-10 of 36 results. Next

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

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