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A198724
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Let P(n) be the maximal prime divisor of 3*n+1. Then a(n) is the smallest number of iterations of P(n) such that the a(n)-th iteration < n, and a(n) = 0, if such number does not exist.
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0
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2, 3, 1, 6, 4, 1, 1, 6, 3, 2, 1, 2, 2, 1, 1, 1, 2, 3, 1, 3, 1, 2, 1, 2, 6, 1, 1, 1, 4, 3, 1, 2, 2, 3, 1, 1, 5, 1, 1, 3, 1, 1, 1, 2, 3, 1, 1, 3, 1, 6, 1, 2, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 3, 2, 1, 1, 2, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1
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OFFSET
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3,1
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COMMENTS
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Question. Is the sequence bounded?
By private communication from Alois P. Heinz, the places of records are 3, 4, 6, 286, 29866 with values 2, 3, 6, 8, 10. No more up to 46000000.
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LINKS
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Table of n, a(n) for n=3..88.
V. Shevelev, Collatz-like problem with prime iterations
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EXAMPLE
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For n=52 we have iterations: P^(1)=157, P^(2)=59, P^(3)=89, P^(4)=67, P^(5)=101, P^(6)=19<52. Thus a(52)=6.
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MATHEMATICA
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P[n_] := FactorInteger[3*n + 1][[-1, 1]]; Table[k = 1; m = n; While[m = P[m]; m >= n, k++]; k, {n, 3, 100}] (* T. D. Noe, Oct 30 2011 *)
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PROG
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(PARI) a(n) = {nb = 1; na = n; while((nna=vecmax(factor(3*na+1)[, 1])) >= n, na = nna; nb++); nb; } \\ Michel Marcus, Feb 06 2016
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CROSSREFS
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Cf. A074473, A126241.
Sequence in context: A166295 A016730 A114576 * A223486 A263294 A205112
Adjacent sequences: A198721 A198722 A198723 * A198725 A198726 A198727
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev, Oct 29 2011
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STATUS
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approved
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