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A319431 The first differences (A319430) of the tribonacci representation numbers (A003726 or A278038) consists of runs of 1's separated by the terms of the present sequence. 2
2, 3, 2, 5, 2, 3, 10, 2, 3, 2, 5, 2, 19, 2, 3, 2, 5, 2, 3, 10, 2, 3, 2, 37, 2, 3, 2, 5, 2, 3, 10, 2, 3, 2, 5, 2, 19, 2, 3, 2, 5, 2, 3, 74, 2, 3, 2, 5, 2, 3, 10, 2, 3, 2, 5, 2, 19, 2, 3, 2, 5, 2, 3, 10, 2, 3, 2, 37, 2, 3, 2, 5, 2, 3, 10, 2, 3, 2, 5, 2, 147, 2, 3, 2, 5, 2, 3, 10, 2, 3, 2, 5, 2, 19, 2, 3, 2, 5, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The runs of 1's in A319430 have lengths that apparently are given by A275925 (with a slight change at the start). The present sequence shows the terms greater than 1.

Let b = "2,3,2", c = "2,3,2,5,2,3", d = "2,3,2,5,2". The sequence appears to consist of a word over the alphabet {b,c,d} interspersed with the sequence 10, 19, 10, 37, 10, 19, 74, 10, 19, 10, 37, 10, 147, 10, 19, 10, 37, 10, ...:

c, 10, d, 19, c, 10, b, 37, c, 10, d, 19, c, 74, c, 10, d, 19, c, 10, b, 37, c, 10, d, 147, c, 10, d, 19, c, 10, b, 37, c, 10, d, 19, c, 74, ...

The interspersed sequence 10, 19, 10, 37, 10, 19, 74, ... appears to have the same kind of structure.

It would be nice to have a recurrence of some kind that produces this sequence.

Needs a bigger b-file.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..1606

EXAMPLE

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22, 24, 25, ... = A003726 (trib. repres. numbers)

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, ... = A319430 (differences)

2, 3, 2, 5, 2, 3, 10, 2, 3, 2, 5, 2, 19, 2, 3, 2, 5, 2, 3, 10, 2, 3, 2, 37, 2, ... (omit 1's, present sequence)

6, 1, 5, 1, 6, 1, 3, 1, 6, 1, 5, 1, 6, 1, 6, 1, 5, 1, 6, 1, 3, 1, 6, 1, 5, 1, ... = run lengths in differences

6, 5, 6, 3, 6, 5, 6, 6, 5, 6, 3, 6, 5, 6, 5, 6, 3, 6, 5, 6, 6, 5, 6, 3, 6, 5, 6, ... = A275925 truncated (BISECTION of run lengths)

CROSSREFS

Cf. A003726, A278038, A319430, A275925.

Sequence in context: A027748 A000705 A073751 * A258581 A108501 A166226

Adjacent sequences:  A319428 A319429 A319430 * A319432 A319433 A319434

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 30 2018

STATUS

approved

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Last modified January 16 15:31 EST 2019. Contains 319195 sequences. (Running on oeis4.)