

A198724


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.


0



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

3,1


COMMENTS

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.


LINKS

Table of n, a(n) for n=3..88.
V. Shevelev, Collatzlike problem with prime iterations


EXAMPLE

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.


MATHEMATICA

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 *)


PROG

(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


CROSSREFS

Cf. A074473, A126241.
Sequence in context: A016730 A319192 A114576 * A223486 A263294 A205112
Adjacent sequences: A198721 A198722 A198723 * A198725 A198726 A198727


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Oct 29 2011


STATUS

approved



