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A377619
a(n) is the number of iterations of x -> 5*x + 2 until (# composites reached) = (# primes reached), starting with prime(n).
1
1, 3, 1, 5, 1, 7, 1, 11, 1, 1, 7, 1, 1, 1, 1, 1, 1, 9, 3, 1, 5, 5, 1, 1, 9, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 1, 3, 1, 3, 1, 9, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 7, 1, 1, 9, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,2
COMMENTS
For a guide to related sequences, see A377609.
EXAMPLE
Starting with prime(1) = 2, we have 5*2+2 = 12; the chain (2,12) has 1 prime and 1 composite. So a(1) = 2-1 = 1.
MATHEMATICA
chain[{start_, u_, v_}] := If[CoprimeQ[u, v] && start*u + v != start,
NestWhile[Append[#, u*Last[#] + v] &, {start}, !
Count[#, _?PrimeQ] == Count[#, _?(! PrimeQ[#] &)] &], {}];
chain[{Prime[1], 5, 2}]
Map[Length[chain[{Prime[#], 5, 2}]] &, Range[1, 100]] - 1
(* Peter J. C. Moses, Oct 31 2024 *)
CROSSREFS
Cf. A377609.
Sequence in context: A300330 A328478 A093411 * A147088 A346468 A340083
KEYWORD
nonn
AUTHOR
Clark Kimberling, Nov 17 2024
STATUS
approved