A065031 -id:A065031 - cp's OEIS frontend

A100961 For a decimal string s, let f(s) = decimal string ijk, where i = number of even digits in s, j = number of odd digits in s, k=i+j (see A171797). Start with s = decimal expansion of n; a(n) = number of applications of f needed to reach the string 123.

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 1, 2, 1, 2

Offset: 0

N. J. A. Sloane, Jun 17 2005

Obviously if the digits of m and n have the same parity then a(m) = a(n). E.g. a(334) = a(110). In other words, a(n) = a(A065031(n)).

It is easy to show that (i) the trajectory of every number under f eventually reaches 123 (if s has more than three digits then f(s) has fewer digits than s) and (ii) since each string ijk has only finitely many preimages, a(n) is unbounded.

			n=0: s=0 -> f(s) = 101 -> f(f(s)) = 123, stop, a(0) = 2.
n=1: s=1 => f(s) = 011 -> f(f(s)) = 123, stop, f(1) = 2.

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

A073054 gives another version. f(n) is (essentially) A171797 or A073053.

Cf. A065031, A308002.

More terms from Zak Seidov, Jun 18 2005

A318700 Positive numbers that contain odd and even digits.

Original entry on oeis.org

10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 114, 116, 118, 120, 121, 122

Offset: 1

Enrique Navarrete, Aug 31 2018

The sequence of first differences takes on the values {1, 2, 3} only, and each of these values occurs infinitely often (the values 1 and 2 are clear; for the value 3, note that consecutive numbers such as 199..9, 200..0 and 399..9, 400..0 that are excluded from the sequence occur infinitely often).
Numbers n such that A065031(n) is a term of A111066. - Felix Fröhlich, Sep 01 2018
Nonnegative integers excluding those such that digits in their decimal representation share all the same parity. - R. J. Cano, Sep 10 2018

			49 and 50 are in the sequence but 19 and 20 are not.

R. J. Cano, PARI program

Cf. A065031, A111066, A030141, A054684, A227870.

Select[Range@ 122, Union[Mod[IntegerDigits[#], 2]] == {0, 1} &] (* Michael De Vlieger, Sep 04 2018 *)

is(n) = my(d=digits(n), v=[]); if(n < 10, return(0)); for(k=1, #d, v=concat(v, [d[k]%2])); vecmin(v)!=vecmax(v) \\ Felix Fröhlich, Sep 01 2018

PARI
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See Cano link.
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A167677 Replace prime digits with 1 and nonprime digits with 2.

Original entry on oeis.org

2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 22, 22, 21, 21, 22, 21, 22, 21, 22, 22, 12, 12, 11, 11, 12, 11, 12, 11, 12, 12, 12, 12, 11, 11, 12, 11, 12, 11, 12, 12, 22, 22, 21, 21, 22, 21, 22, 21, 22, 22, 12, 12, 11, 11, 12, 11, 12, 11, 12, 12, 22, 22, 21, 21, 22, 21, 22, 21, 22, 22, 12, 12, 11

Offset: 0

Zak Seidov, Nov 09 2009

Cf. A065031, A167678, A167679.

Table[FromDigits[If[PrimeQ[ # ],1,2]&/@IntegerDigits[n]],{n,0,200}]

A167678 Replace prime digits with 2 and nonprime digits with 1.

Original entry on oeis.org

1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 11, 11, 12, 12, 11, 12, 11, 12, 11, 11, 21, 21, 22, 22, 21, 22, 21, 22, 21, 21, 21, 21, 22, 22, 21, 22, 21, 22, 21, 21, 11, 11, 12, 12, 11, 12, 11, 12, 11, 11, 21, 21, 22, 22, 21, 22, 21, 22, 21, 21, 11, 11, 12, 12, 11, 12, 11, 12, 11, 11, 21, 21, 22

Offset: 0

Zak Seidov, Nov 09 2009

Cf. A065031, A167677, A167679.

Table[FromDigits[If[PrimeQ[ # ],2,1]&/@IntegerDigits[n]],{n,0,200}]

A167679 Replace odd digits with 2 and even digits with 1.

Original entry on oeis.org

1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 21, 22, 21, 22, 21, 22, 21, 22, 21, 22, 11, 12, 11, 12, 11, 12, 11, 12, 11, 12, 21, 22, 21, 22, 21, 22, 21, 22, 21, 22, 11, 12, 11, 12, 11, 12, 11, 12, 11, 12, 21, 22, 21, 22, 21, 22, 21, 22, 21, 22, 11, 12, 11, 12, 11, 12, 11, 12, 11, 12, 21, 22, 21

Offset: 0

Zak Seidov, Nov 09 2009

Cf. A065031, A167677, A167678.

Table[FromDigits[If[OddQ[ # ],2,1]&/@IntegerDigits[n]],{n,0,200}]

cp's OEIS Frontend

A100961 For a decimal string s, let f(s) = decimal string ijk, where i = number of even digits in s, j = number of odd digits in s, k=i+j (see A171797). Start with s = decimal expansion of n; a(n) = number of applications of f needed to reach the string 123.

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A318700 Positive numbers that contain odd and even digits.

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Author

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Comments

Examples

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Programs

Mathematica

PARI

PARI

A167677 Replace prime digits with 1 and nonprime digits with 2.

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Author

Keywords

Crossrefs

Programs

Mathematica

A167678 Replace prime digits with 2 and nonprime digits with 1.

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Author

Keywords

Crossrefs

Programs

Mathematica

A167679 Replace odd digits with 2 and even digits with 1.

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Author

Keywords

Crossrefs

Programs

Mathematica