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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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A016730 A319192 A114576 * A223486 A205112 A173161
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Oct 29 2011
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)