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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 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 April 10 10:25 EDT 2021. Contains 342845 sequences. (Running on oeis4.)