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A352089
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Tribonacci-Niven numbers: numbers that are divisible by the number of terms in their minimal (or greedy) representation in terms of the tribonacci numbers (A278038).
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8
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1, 2, 4, 6, 7, 8, 12, 13, 14, 18, 20, 21, 24, 26, 27, 28, 30, 33, 36, 39, 40, 44, 46, 48, 56, 60, 68, 69, 72, 75, 76, 80, 81, 82, 84, 87, 88, 90, 94, 96, 100, 108, 115, 116, 120, 126, 128, 129, 132, 135, 136, 138, 140, 149, 150, 156, 162, 168, 174, 176, 177, 180
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OFFSET
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1,2
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COMMENTS
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Numbers k such that A278043(k) | k.
The positive tribonacci numbers (A000073) are all terms.
If k = A000073(A042964(m)) is an odd tribonacci number, then k+1 is a term.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
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EXAMPLE
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6 is a term since its minimal tribonacci representation, A278038(6) = 110, has A278043(6) = 2 1's and 6 is divisible by 2.
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MATHEMATICA
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t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; q[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; AppendTo[s, k]; m -= t[k]; k = 1]; Divisible[n, DigitCount[Total[2^(s - 1)], 2, 1]]]; Select[Range[180], q]
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CROSSREFS
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Cf. A000073, A042964, A278038, A278043.
Subsequences: A352090, A352091, A352092.
Similar sequences: A005349, A049445, A064150, A064438, A064481, A118363, A328208, A328212, A331085, A333426, A342726, A334308, A331728, A342426, A344341, A351714, A351719.
Sequence in context: A186112 A029453 A330943 * A358458 A014855 A298479
Adjacent sequences: A352086 A352087 A352088 * A352090 A352091 A352092
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KEYWORD
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nonn,base
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AUTHOR
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Amiram Eldar, Mar 04 2022
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STATUS
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approved
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