

A082449


Let f(p) = greatest prime divisor of p1. Sequence gives smallest prime which takes at least n steps to reach 2 when f is iterated.


4



2, 3, 7, 23, 47, 283, 719, 1439, 2879, 34549, 138197, 1266767, 14619833, 36449279, 377982107, 1432349099, 22111003847
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OFFSET

0,1


COMMENTS

There is a remarkable and unexplained agreement: if 3 and 7 are replaced by 11 and 14619833 is replaced by 14920303, the result is sequence A056637 (least prime of class n, according to the ErdősSelfridge classification of primes).
From David A. Corneth, Oct 18 2016 (Start):
If a(n) * k + 1 is prime then a(n + 1) <= a(n) * k + 1.
a(18), a(19), ..., a(23) <= 309554053859, 619108107719, 19811459447009, 433142367554861, 866284735109723, 22523403112852799 respectively. (End)


REFERENCES

Steven G. Johnson, Postings to Number Theory List, Apr 23 and Apr 25, 2003.


LINKS

Table of n, a(n) for n=0..16.


EXAMPLE

a(2) = 7 since 7 > 3 > 2 takes two steps, and smaller primes require less than 2 steps.
For p = 2879, 8 steps are needed (2879 > 1439 > 719 > 359 > 179 > 89 > 11 > 5 > 2), so a(8) = 2879, since smaller primes require less than 8 steps.


MAPLE

with(numtheory);
P:=proc(i)
local b, c, d, k, n, p; c:=1;
for n from 1 to i do k:=1; b:=ithprime(n);
while b>1 do k:=k+1; p:=ifactors(b)[2]; b:=mul((op(1, d)1)^op(2, d), d=p); od;
if k>c then c:=k; print(ithprime(n)); fi;
od; end: # Paolo P. Lava, Feb 16 2012


MATHEMATICA

(* Assuming a(n) > 2 a(n1) if n>1 *) Clear[a, f]; f[p_] := FactorInteger[p  1][[1, 1]]; f[2] = 2; a[n_] := a[n] = For[p = NextPrime[2 a[n1]], True, p = NextPrime[p], k = 0; If[Length[FixedPointList[f, p]] == n+2, Return[p]]]; a[0]=2; a[1]=3; Table[Print[a[n]]; a[n], {n, 0, 16}] (* JeanFrançois Alcover, Oct 18 2016 *)


CROSSREFS

Cf. A006530, A023503, A083647, A056637, A083647.
Sequence in context: A000057 A037231 A248525 * A129741 A006720 A084710
Adjacent sequences: A082446 A082447 A082448 * A082450 A082451 A082452


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane, Apr 25 2003


EXTENSIONS

Edited by Klaus Brockhaus, May 01 2003
a(16) from Donovan Johnson, Nov 17 2008


STATUS

approved



