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, 3, 7, 9, 17, 37, 77

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

Table of n, a(n) for n=1..7.

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: A360251 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