A021895 -id:A021895 - cp's OEIS frontend

A106747 Replace each odd digit d of n with (d-1)/2 and each even digit d with d/2.

0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 30, 30, 31, 31, 32, 32

Offset: 0

Zak Seidov, May 12 2005

Terms are repeated. Differs from A004526 and A021895 starting with a(11)=0, A004526(11)=A021895(11)=5.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A004526, A021895, A107128, A107130.

a106747 n = if n == 0 then 0 else 10 * (a106747 n') + div d 2
            where (n', d) = divMod n 10
-- Reinhard Zumkeller, Jan 14 2015

a[n_]:=FromDigits[Map[If[Mod[ #, 2]==1, (#-1)/2, #/2]&, IntegerDigits[n]]];Table[a[n], {n, 0, 100}]

def A106747(n): return int(str(n).translate({49:48,50:49,51:49,52:50,53:50,54:51,55:51,56:52,57:52})) # Chai Wah Wu, Apr 07 2022

A113675 Decimal expansion of 1/8991.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4

Offset: 0

Daisuke Minematsu and Ryohei Miyadera, Jan 17 2006

1/(89...91) can produce this kind of sequence infinitely.

			0.00011122233344455566677788900011...

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See pp. 60, 308.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A002264, A021895.

m = 17; Sqrt[Apply[Plus, 576*Table[(10^3)^k, {k, 0, m}]]]
Join[{0,0,0},RealDigits[1/8991,10,120][[1]]] (* Harvey P. Dale, Apr 22 2012 *)

sqrt(576576576576576576576576576576576576576576576576576576) = 72*sqrt(111222333444555666777889000111222333444555666777889).

G.f.: x^3*(Sum_{i=0..27} floor((i+3)/3)*x^i + x^23 - 9*x^24*(1 + x + x^2 + 10*x^3/9))/(1 - x^27). - Stefano Spezia, Jul 31 2024

A113694 Decimal expansion of 10/44955.

Original entry on oeis.org

0, 0, 0, 2, 2, 2, 4, 4, 4, 6, 6, 6, 8, 8, 9, 1, 1, 1, 3, 3, 3, 5, 5, 5, 7, 7, 8, 0, 0, 0, 2, 2, 2, 4, 4, 4, 6, 6, 6, 8, 8, 9, 1, 1, 1, 3, 3, 3, 5, 5, 5, 7, 7, 8, 0, 0, 0, 2, 2, 2, 4, 4, 4, 6, 6, 6, 8, 8, 9, 1, 1, 1, 3, 3, 3, 5, 5, 5, 7, 7, 8, 0, 0, 0, 2, 2, 2, 4, 4, 4, 6, 6, 6, 8, 8, 9, 1, 1, 1, 3, 3, 3, 5, 5, 5, 7, 7, 8

Offset: 0

Daisuke Minematsu and Ryohei Miyadera, Jan 17 2006

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A021895, A021085.

Join[{0,0,0},RealDigits[10/44955,10,120][[1]]] (* Harvey P. Dale, May 13 2012 *)

A113657 Decimal expansion of 1/1089.

Original entry on oeis.org

0, 0, 0, 9, 1, 8, 2, 7, 3, 6, 4, 5, 5, 4, 6, 3, 7, 2, 8, 1, 9, 1, 0, 0, 0, 9, 1, 8, 2, 7, 3, 6, 4, 5, 5, 4, 6, 3, 7, 2, 8, 1, 9, 1, 0, 0, 0, 9, 1, 8, 2, 7, 3, 6, 4, 5, 5, 4, 6, 3, 7, 2, 8, 1, 9, 1, 0, 0, 0, 9, 1, 8, 2, 7, 3, 6, 4, 5, 5, 4, 6, 3, 7, 2, 8, 1, 9, 1, 0, 0, 0, 9, 1, 8, 2, 7, 3, 6

Offset: 0

Ryohei Miyadera, Jan 16 2006

This sequence can also be produced by Sqrt[11111111111111111111111111111111111111111111] =11*Sqrt[91827364554637281910009182736455463728191], where Sqrt is the square root. In fact we found this from the square root and later looked for the same sequence in the expansion.
Comment from Eric Desbiaux, Apr 08 2008: Also, of course, decimal expansion of 9/9801. Note that
99/9801 = 0.0101010101010101010101...,
9999/9801 = 1.02020202020202020202020...,
999999/9801 = 102.0303030303030303030303...,
99999999/9801 = 10203.040404040404040404040404..., etc.

			0.0009182736455463728191000918273645546372819100091827364554...

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A137301-A137304.

Cf. A021895, A021085.

m = 21; Sqrt[Apply[Plus, Table[11*100^k, {k, 0, m}]]]

Edited by N. J. A. Sloane, May 15 2008, at the suggestion of R. J. Mathar.

A113818 Decimal expansion of the integer (101101101101101101101101101)/9.

Original entry on oeis.org

1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 9, 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 9

Offset: 26

Ryohei Miyadera and Daisuke Minematsu, Jan 23 2006

Using square roots and periodic numbers you can produce this kind of curious sequence.

			(101101101101101101101101101)/9 = 11233455677900122344566789.

R. Miyadera, Interesting patterns made by periodic numbers and square root.

Cf. A021085, A021895, A113694, A113675.

RealDigits[101101101101101101101101101/9,10,26][[1]] (* Harvey P. Dale, May 21 2020 *)

(101101101101101101101101101)/9 or Sqrt[101101101101101101101101101], where sqrt is the square root.

Edited by N. J. A. Sloane, May 26 2006

Previous Mathematica program replaced by Harvey P. Dale, May 21 2020

A114054 Decimal expansion of 998998998998998998998998998/9.

Original entry on oeis.org

1, 1, 0, 9, 9, 9, 8, 8, 8, 7, 7, 7, 6, 6, 6, 5, 5, 5, 4, 4, 4, 3, 3, 3, 2, 2, 2

Offset: 27

Satoshi Hashiba and Ryohei Miyadera, Feb 02 2006

We have found out that we can generate many interesting sequences with periodic numbers and square roots.

Cf. A021895, A113694, A113675.

{998998998998998998998998998/9,Sqrt[998998998998998998998998998]}

998998998998998998998998998/9 or sqrt(998998998998998998998998998)=3*sqrt(110999888777666555444333222), where sqrt is the square root.

A115595 The sequence 11,0,1,3333,2,3,5555,4,5,7777,6,7,9999,9,0,2222,1,2,4444,3,4,6666,5,6,8888,7,9,11 has three subsequences that have interesting patterns inside it. Namely, 11,0,(1),3333,2,(3),5555,4,(5),7777,6,(7),9999,9,(0),2222,1,(2),4444,3,(4),6666,5,(6),8888,7,(9),11.

Original entry on oeis.org

11, 0, 1, 3333, 2, 3, 5555, 4, 5, 7777, 6, 7, 9999, 9, 0, 2222, 1, 2, 4444, 3, 4, 6666, 5, 6, 8888, 7, 9, 11

Offset: 1

Satoshi Hashiba (fantasia_sato205(AT)kcc.zaq.ne.jp), Mar 10 2006

You can generate very interesting sequences by using periodic numbers and the square root.

Cf. A021895, A021085, A113675, A113694.

Sqrt[991199991199991199991199991199991199991199991199991199]

You can get this sequence by Sqrt[991199991199991199991199991199991199991199991199991199], where Sqrt is the square root. Or (991199991199991199991199991199991199991199991199991199)/9.

cp's OEIS Frontend

A106747 Replace each odd digit d of n with (d-1)/2 and each even digit d with d/2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Mathematica

Python

A113675 Decimal expansion of 1/8991.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

Formula

A113694 Decimal expansion of 10/44955.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A113657 Decimal expansion of 1/1089.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A113818 Decimal expansion of the integer (101101101101101101101101101)/9.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A114054 Decimal expansion of 998998998998998998998998998/9.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

A115595 The sequence 11,0,1,3333,2,3,5555,4,5,7777,6,7,9999,9,0,2222,1,2,4444,3,4,6666,5,6,8888,7,9,11 has three subsequences that have interesting patterns inside it. Namely, 11,0,(1),3333,2,(3),5555,4,(5),7777,6,(7),9999,9,(0),2222,1,(2),4444,3,(4),6666,5,(6),8888,7,(9),11.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula