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A377614
a(n) is the number of iterations of x -> 2*x + 5 until (# composites reached) = (# primes reached), starting with prime(n).
1
1, 11, 1, 15, 1, 17, 1, 3, 1, 1, 15, 17, 1, 1, 1, 1, 1, 13, 13, 1, 19, 7, 1, 1, 13, 1, 15, 1, 7, 1, 1, 1, 1, 9, 1, 17, 1, 3, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 3, 1, 1, 1, 1, 5, 1, 1, 3, 1, 3, 1, 5, 1, 1, 1, 1, 1, 1, 1, 7, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1
OFFSET
1,2
COMMENTS
For a guide to related sequences, see A377609.
EXAMPLE
Starting with prime(1) = 2, we have 2*2+5 = 9; the chain (2,9) 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[#] &)] &];
chain[{Prime[1], 2, 5}]
Map[Length[chain[{Prime[#], 2, 5}]] &, Range[100]] - 1
(* Peter J. C. Moses Oct 31 2024 *)
CROSSREFS
Cf. A377609.
Sequence in context: A281096 A280506 A222803 * A201132 A212488 A373821
KEYWORD
nonn
AUTHOR
Clark Kimberling, Nov 13 2024
STATUS
approved