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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. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..50000 (first 1606 terms from N. J. A. Sloane) 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) MATHEMATICA DeleteCases[Differences@ Select[Range[0, 1200], SequenceCount[IntegerDigits[#, 2], {1, 1, 1}] == 0 &] , 1] (* Michael De Vlieger, Dec 23 2019 *) CROSSREFS Cf. A003726, A275925, A278038, A319430. Sequence in context: A328852 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 December 5 17:28 EST 2021. Contains 349557 sequences. (Running on oeis4.)