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 A165803 Integers n such that the trajectory of n under repeated applications of the map k->(k-3)/2 is a chain of primes that reaches 2 or 3 (n itself need not be a prime). 2
 2, 3, 7, 9, 17, 37, 77 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For initial values n > 3, the map is applied at least once, so 9 is in the sequence although it is not a prime. The sequence consists of p = 2 and p = 3 and the two finite chains of primes that are formed by repeated application of p -> 2*p + 3, which are 2 -> 7 -> 17 -> 37 -> 77 and 3 -> 9. LINKS EXAMPLE (77-3)/2 = 37 (prime); (37-3)/2 = 17 (prime); (17-3)/2 = 7 (prime); (7-3)/2 = 2; stop (because 2 has been reached). MATHEMATICA f[n_] := Module[{k = n}, While[k > 3, k = (k - 3)/2; If[ !PrimeQ[k], Break[]]]; PrimeQ[k]]; A165803 = {}; Do[If[f[n], AppendTo[A165803, n]], {n, 5!}]; A165803 cpQ[n_]:=AllTrue[Rest[NestWhileList[(#-3)/2&, n, #!=2&&#!=3&, 1, 20]], PrimeQ]; Select[Range[100], cpQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 24 2019 *) CROSSREFS Cf. A165801, A165802 Sequence in context: A075855 A140189 A327066 * A327779 A291740 A204520 Adjacent sequences:  A165800 A165801 A165802 * A165804 A165805 A165806 KEYWORD nonn,fini,full AUTHOR Vladimir Joseph Stephan Orlovsky, Sep 28 2009 EXTENSIONS Edited by Jon E. Schoenfield, Dec 01 2013 Further edited by N. J. A. Sloane, Dec 02 2013 STATUS approved

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Last modified June 12 12:53 EDT 2021. Contains 344947 sequences. (Running on oeis4.)