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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
1, 2, 9, 122, 1357323 (list; graph; refs; listen; history; text; internal format)
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 * A088862 A062457 A067966

Adjacent sequences:  A135540 A135541 A135542 * A135544 A135545 A135546

KEYWORD

hard,more,nonn

AUTHOR

Sergio Pimentel, Feb 22 2008

STATUS

approved

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Last modified June 25 20:26 EDT 2017. Contains 288730 sequences.