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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Nov 17 2024
STATUS
approved