A165803 - OEIS

%I #18 Jul 24 2019 16:30:17

%S 2,3,7,9,17,37,77

%N 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).

%C 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.

%e (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).

%t 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

%t 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 *)

%Y Cf. A165801, A165802

%K nonn,fini,full

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Sep 28 2009

%E Edited by _Jon E. Schoenfield_, Dec 01 2013

%E Further edited by _N. J. A. Sloane_, Dec 02 2013