A169863 -id:A169863 - cp's OEIS frontend

A169864 The sequence S of a pair S, T generalizing Golomb's sequence A001462 and the pair A093848, A169863. See Comments for definition.

1, 3, 4, 6, 8, 10, 12, 13, 15, 17, 19, 21, 23, 25, 26, 28, 30, 32, 34, 36, 38, 40, 42, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 91, 93

Offset: 1

N. J. A. Sloane, Jun 27 2010, following a posting from Eric Angelini to the Sequence Fans Mailing List, Jun 22, 2010

S is built with the rules [1] that you cannot insert any integer between two "touching" runs (run 1,3 is followed by 4,6,8,10,12; there is no integer between 3 and 4) and [2] that S and T share no integer.
T encodes the instructions for S.
It is not quite clear to me if T is the complement of S, or is merely disjoint from it.

Cf. A169865, A001462, A093848, A169863, A169866, A169867.

A169865 The sequence T of a pair S, T generalizing Golomb's sequence A001462 and the pair A093848, A169863. See Comments for definition.

Original entry on oeis.org

2, 5, 7, 9, 11, 14, 16, 18, 20, 22, 24, 27, 29, 31, 33, 35, 37, 39, 41, 44, 46

Offset: 1

N. J. A. Sloane, Jun 27 2010, following a posting from Eric Angelini to the Sequence Fans Mailing List, Jun 22, 2010

S is built with the rules [1] that you cannot insert any integer between two "touching" runs (run 1,3 is followed by 4,6,8,10,12; there is no integer between 3 and 4) and [2] that S and T share no integer.

Cf. A169864, A001462, A093848, A169863.

A169866 The sequence S of a pair of complementary sequences (S, T) which are similar to the pairs (A093848, A169863), (A169864, A169865), except that here the lengths of the equal-parity runs of one sequence are given by the other.

Original entry on oeis.org

1, 3, 4, 6, 8, 10, 12, 11, 13, 15, 17, 19, 21, 23, 22, 24, 26, 28, 30, 32, 34, 36, 38, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86

Offset: 1

N. J. A. Sloane, Jun 27 2010, following a posting from Eric Angelini to the Sequence Fans Mailing List, Jun 22, 2010

Cf. A169867, A001462, A093848, A169863, A169864, A169865.

A169867 The sequence T of a pair of complementary sequences (S, T) which are similar to the pairs (A093848, A169863), (A169864, A169865), except that here the lengths of the equal-parity runs of one sequence are given by the other.

Original entry on oeis.org

2, 5, 7, 9, 14, 16, 18, 20, 25, 27, 29, 31, 33, 35, 40, 42, 44, 46, 48, 50, 52, 54, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110

Offset: 1

N. J. A. Sloane, Jun 27 2010, following a posting from Eric Angelini to the Sequence Fans Mailing List, Jun 22, 2010

Cf. A169866, A001462, A093848, A169863, A169864, A169865.

A093848 (a(n)) is the earliest monotonic sequence starting with a(1)=1 and satisfying a(n)=length of n-th run of consecutive integers with same parity.

Original entry on oeis.org

1, 2, 4, 5, 7, 9, 11, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 31, 33, 34, 36, 38, 40, 42, 44, 46, 48, 50, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 122, 124

Offset: 1

Benoit Cloitre, May 21 2004

nonn

There are a(1) odd terms, a(2) even terms, a(3) odd terms, a(4) even terms ... - Benoit Cloitre, May 26 2004

A variation on Golomb's sequence A001462.

			Sequence begins: (1),(2,4),(5,7,9,11),(12,14,16,18,20),(21,.... since the number of elements in each run of odd or even integers is 1, 2, 4, 5, ... the sequence itself.

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A001462, A049039, A169863.

A093848 := proc(nmax) local n,par,a,alast,j ; n := 3 ; par := 1 ; a := [1,2,4] ; while nops(a) < nmax do alast := op(-1,a); if type(alast,'even') = type(par,'even') then ; else alast := alast -1 ; end if; for j from 1 to op(n,a) do a := [op(a), alast+2*j] ; end do: par := 1-par ; n := n+1 ; end do: a ; end proc: A093848(120) ; # R. J. Mathar, Jun 22 2010

t={1,2,4}; Do[t=Join[t,Table[t[[-1]]+2*i-1, {i,t[[n]]}]], {n,3,40}]

it seems that a(n) = 2n - a*n^b + o(n^b) where a and b are 2 suitable constants. b=0.4.... Does b=2-phi where phi is the golden ratio?

Terms starting at a(52) corrected by R. J. Mathar, Jun 22 2010

cp's OEIS Frontend

A169864 The sequence S of a pair S, T generalizing Golomb's sequence A001462 and the pair A093848, A169863. See Comments for definition.

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A169865 The sequence T of a pair S, T generalizing Golomb's sequence A001462 and the pair A093848, A169863. See Comments for definition.

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A169866 The sequence S of a pair of complementary sequences (S, T) which are similar to the pairs (A093848, A169863), (A169864, A169865), except that here the lengths of the equal-parity runs of one sequence are given by the other.

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A169867 The sequence T of a pair of complementary sequences (S, T) which are similar to the pairs (A093848, A169863), (A169864, A169865), except that here the lengths of the equal-parity runs of one sequence are given by the other.

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A093848 (a(n)) is the earliest monotonic sequence starting with a(1)=1 and satisfying a(n)=length of n-th run of consecutive integers with same parity.

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