

A135543


Record number of steps under iterations of "map n to n  (largest prime <= n)" (A064722) until reaching the limiting value 0 or 1. Also, places where A121561 reaches a new record.


1




OFFSET

0,2


COMMENTS

a(5) must be very large (>100000000). Can anyone extend the sequence?
Conjecture: a(n) is not equal A175079(n)  1 for all n >= 1. [From Jaroslav Krizek, Feb 05 2010]


LINKS

Table of n, a(n) for n=0..4.


FORMULA

Iterate n  (largest prime <= n) until reaching 0 or 1. Count the # of iterations required to reach 0 or 1 and determine if it is a new record.


EXAMPLE

a(4) = 1357323 because after iterating n  (largest prime <= n) we get:
1357323  1357201 = 122 =>
122  113 = 9 =>
9  7 = 2 =>
2  2 = 0,
which takes 4 steps.


MATHEMATICA

LrgstPrm[n_] := Block[{k = n}, While[ !PrimeQ@ k, k ]; k]; f[n_] := Block[{c = 0, d = n}, While[d > 1, d = d  LrgstPrm@d; c++ ]; c]; lst = {}; record = 1; Do[ a = f@n; If[a > record, record = a; AppendTo[lst, a]; Print@ n], {n, 100}] (* Robert G. Wilson v *)


CROSSREFS

Cf. A121559, A121560, A064722, A121561, A121560, A064722.
Sequence in context: A067965 A237999 A194017 * A316855 A088862 A062457
Adjacent sequences: A135540 A135541 A135542 * A135544 A135545 A135546


KEYWORD

hard,more,nonn


AUTHOR

Sergio Pimentel, Feb 22 2008


STATUS

approved



