A377616 - OEIS

A377616

a(n) is the number of iterations of x -> 3*x + 2 until (# composites reached) = (# primes reached), starting with prime(n).

1, 9, 5, 7, 1, 3, 3, 7, 5, 11, 1, 3, 1, 7, 1, 1, 5, 1, 1, 1, 1, 5, 13, 5, 11, 1, 3, 1, 1, 1, 5, 1, 1, 31, 7, 1, 1, 3, 9, 3, 1, 1, 1, 1, 3, 5, 1, 1, 3, 1, 5, 3, 1, 1, 3, 1, 3, 1, 1, 1, 1, 9, 1, 1, 3, 5, 1, 5, 1, 3, 3, 1, 3, 1, 1, 3, 1, 11, 1, 5, 29, 1, 1, 7

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OFFSET

1,2

COMMENTS

For a guide to related sequences, see A377609.

LINKS

Table of n, a(n) for n=1..84.

EXAMPLE

Starting with prime(1) = 2, we have 2*2+2 = 6; the chain (2,6) has 1 prime and 1 composite. So a(1) = 2-1 = 1.

MATHEMATICA

chain[{start_, u_, v_}] := NestWhile[Append[#, u*Last[#] + v] &, {start}, !

Count[#, _?PrimeQ] == Count[#, _?(! PrimeQ[#] &)] &];