A026242 -id:A026242 - cp's OEIS frontend

A307669 Lexicographically earliest sequence of positive terms, such that each value, say v, appears five times at indices k, k + v, k + 2v, k + 3v and k + 4*v for some k.

1, 1, 1, 1, 1, 2, 4, 2, 8, 2, 4, 2, 9, 2, 4, 10, 8, 3, 4, 14, 3, 9, 4, 3, 8, 10, 3, 11, 13, 3, 9, 19, 8, 14, 12, 10, 15, 20, 11, 9, 8, 13, 17, 21, 24, 10, 12, 14, 9, 11, 19, 15, 26, 30, 13, 10, 23, 20, 12, 17, 11, 14, 25, 28, 21, 29, 15, 13, 24, 19, 12, 11, 18

Offset: 1

Rémy Sigrist, Apr 20 2019

nonn

This sequence is a variant of A307664.
Graphically, we have five chaotic lines.
Apparently every positive integer appears in the sequence.

			For n = 1:
- we can set a(1) = a(2) = a(3) = a(4) = a(5) = 1.
For n = 6:
- we can set a(6) = a(8) = a(10) = a(12) = a(14) = 2.
For n = 7:
- a(10) is already known, hence a(7) <> 3,
- we can set a(7) = a(11) = a(15) = a(19) = a(23) = 4.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Colored scatterplot of the first 250000 terms (where the color is based on the ordinal transform of the sequence)
Rémy Sigrist, PARI program for A307669

Cf. A026242, A307664.

PARI
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See Links section.
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A214371 If a(n) has not yet been defined then set a(n) = least positive integer that has not yet occurred; also if n>1 and a(n+a(n)) has not yet been defined then set a(n+a(n)) = a(n).

Original entry on oeis.org

1, 2, 3, 2, 4, 3, 5, 6, 4, 7, 8, 5, 4, 6, 9, 10, 7, 11, 8, 6, 12, 13, 14, 9, 15, 10, 8, 16, 11, 17, 18, 19, 12, 20, 13, 10, 14, 21, 22, 15, 23, 24, 25, 16, 12, 10, 17, 13, 18, 26, 19, 27, 28, 20, 15, 10, 12, 29, 21, 16, 22, 30, 31, 23, 32, 24, 18, 25, 12, 19, 33

Offset: 1

Alex Ratushnyak, Jul 14 2012

Cf. A214370.

Cf. A026242, A026338.

mex[a_]:=Module[{q}, q=1; While[MemberQ[a,q], q++]; q]; a = Table[0,{k, 1, 100}]; For[n=1, n<=100, n++, {If[a[[n]]==0, a[[n]] = mex[a]]; If[n>1, {nan = n+a[[n]]; If[(nan <= Length[a]) && (a[[nan]] == 0), a[[nan]] = a[[n]]]}]; }]; a

SIZE = 300
a = [-8]*SIZE
top=0
for n in range(SIZE):
    if a[n]==-8:       # if a[n] is undefined yet
        top+=1
        a[n]=top
    if 1

a(1)=1, for n>1, a(n) = A214370(n-1)+1.

A336200 Lexicographically earliest sequence of distinct terms such that every integer k appears twice, at distance a(k).

Original entry on oeis.org

1, 1, 2, 2, 3, 4, 3, 4, 5, 6, 8, 5, 7, 6, 8, 7, 9, 10, 11, 12, 13, 9, 14, 10, 12, 15, 11, 13, 14, 16, 17, 18, 19, 15, 20, 21, 16, 23, 22, 17, 24, 18, 25, 19, 26, 27, 20, 22, 21, 28, 24, 23, 29, 30, 25, 31, 27, 32, 33, 26, 35, 34, 28, 36, 38, 37, 29, 39, 40, 30

Offset: 1

Rémy Sigrist, Jul 11 2020

nonn

This sequence combines features of A001462 and of A026242.

			For n = 1:
- we can choose a(1) = 1,
- and then a(1+a(1)) = a(2) = 1.
For n = 3:
- we can choose a(3) = 2,
- and then a(3+a(2)) = a(4) = 2.
For n = 5:
- we can choose a(5) = 3,
- and then a(5+a(3)) = a(7) = 3.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A336200

Cf. A001462, A026242.

PARI
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See Links section.
```

A117407 a(n) = j if n is T(j), else a(n) = k if n is U(k), where T is a Beatty sequence based on (sqrt(5)+5)/2 (A054770) and U is its complement (A063732).

Original entry on oeis.org

1, 2, 1, 3, 4, 5, 2, 6, 7, 3, 8, 9, 10, 4, 11, 12, 13, 5, 14, 15, 6, 16, 17, 18, 7, 19, 20, 8, 21, 22, 23, 9, 24, 25, 26, 10, 27, 28, 11, 29, 30, 31, 12, 32, 33, 34, 13, 35, 36, 14, 37, 38, 39, 15, 40, 41, 16, 42, 43, 44, 17, 45, 46, 47, 18, 48, 49, 19, 50, 51, 52, 20, 53, 54, 21, 55

Offset: 0

Casey Mongoven, Mar 13 2006

nonn

Every positive integer occurs exactly twice. Taking a Lucas number (A000032) of terms L(n) starting at a(0), the last two terms are a pair of Fibonacci numbers (A000045). If n is even, then the last two terms are F(n+1) followed by F(n-1), if n is odd they are F(n-1) followed by F(n+1), where F is the Fibonacci sequence. For example, the first L(4) = 7 terms of this sequence are (1,2,1,3,4,5,2) and the last members are 5 and 2 which are equal to F(5) and F(3). Note also that L(n) = F(n-1) + F(n+1).

			a(9) = 3 because 9 = T(3).

Cf. A026272, A026242.

cp's OEIS Frontend

A307669 Lexicographically earliest sequence of positive terms, such that each value, say v, appears five times at indices k, k + v, k + 2v, k + 3v and k + 4*v for some k.

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A214371 If a(n) has not yet been defined then set a(n) = least positive integer that has not yet occurred; also if n>1 and a(n+a(n)) has not yet been defined then set a(n+a(n)) = a(n).

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A336200 Lexicographically earliest sequence of distinct terms such that every integer k appears twice, at distance a(k).

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Author

Keywords

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Examples

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Crossrefs

Programs

PARI

A117407 a(n) = j if n is T(j), else a(n) = k if n is U(k), where T is a Beatty sequence based on (sqrt(5)+5)/2 (A054770) and U is its complement (A063732).

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Author

Keywords

Comments

Examples

Crossrefs

cp's OEIS Frontend

A307669 Lexicographically earliest sequence of positive terms, such that each value, say v, appears five times at indices k, k + v, k + 2*v, k + 3*v and k + 4*v for some k.

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Author

Keywords

Comments

Examples

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Programs

PARI

A214371 If a(n) has not yet been defined then set a(n) = least positive integer that has not yet occurred; also if n>1 and a(n+a(n)) has not yet been defined then set a(n+a(n)) = a(n).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Python

Formula

A336200 Lexicographically earliest sequence of distinct terms such that every integer k appears twice, at distance a(k).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A117407 a(n) = j if n is T(j), else a(n) = k if n is U(k), where T is a Beatty sequence based on (sqrt(5)+5)/2 (A054770) and U is its complement (A063732).

Views

Author

Keywords

Comments

Examples

Crossrefs

A307669 Lexicographically earliest sequence of positive terms, such that each value, say v, appears five times at indices k, k + v, k + 2v, k + 3v and k + 4*v for some k.