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A325610 Adjusted frequency depth of 2^n - 1. 7
0, 1, 1, 3, 1, 4, 1, 3, 3, 3, 3, 5, 1, 3, 3, 3, 1, 5, 1, 5, 5, 3, 3, 5, 3, 3, 3, 3, 3, 5, 1, 3, 3, 3, 3, 5, 3, 3, 3, 5, 3, 5, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 5, 1, 3, 5, 3, 3, 5, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 5, 3, 5, 3, 3, 3, 5, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The adjusted frequency depth of a positive integer n is 0 if n = 1, and otherwise it is 1 plus the number of times one must apply A181819 to reach a prime number, where A181819(k = p^i*...*q^j) = prime(i)*...*prime(j) = product of primes indexed by the prime exponents of k. For example, 180 has adjusted frequency depth 5 because we have: 180 -> 18 -> 6 -> 4 -> 3.

LINKS

Table of n, a(n) for n=1..87.

MATHEMATICA

fdadj[ptn_List]:=If[ptn=={}, 0, Length[NestWhileList[Sort[Length/@Split[#1]]&, ptn, Length[#1]>1&]]];

Table[fdadj[2^n-1], {n, 100}]

CROSSREFS

Cf. A001222, A001221, A056239, A071625, A112798, A323014, A325280.

Mersenne numbers: A046051, A046800, A059305, A325611, A325612, A325625.

Sequence in context: A165595 A213181 A301848 * A278536 A143825 A290478

Adjacent sequences:  A325607 A325608 A325609 * A325611 A325612 A325613

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 12 2019

STATUS

approved

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Last modified June 13 13:08 EDT 2021. Contains 344997 sequences. (Running on oeis4.)