A138757 a(n) = A007918(A138750(n)), that is, least prime > n/2 if n=2 (mod 3), > 2n otherwise.

2, 2, 2, 7, 11, 3, 13, 17, 5, 19, 23, 7, 29, 29, 7, 31, 37, 11, 37, 41, 11, 43, 47, 13, 53, 53, 13, 59, 59, 17, 61, 67, 17, 67, 71, 19, 73, 79, 19, 79, 83, 23, 89, 89, 23, 97, 97, 29, 97, 101, 29, 103, 107, 29, 109, 113, 29, 127, 127, 31, 127, 127, 31, 127

Offset

0,1

Comments

This can be considered as an analog of the Collatz (or 3n+1) map on the set of primes, see A138751 and A138754 for details.

Numbers 0,1,2 go immediately to the unique fixed point 2, all others end up in the cycle 7 -> 17 -> 11 -> 7, after a number of iterations given by A138753(A138757(n))-1 (= A138753(n)-2 if n is prime).

Links

Table of n, a(n) for n=0..63.

Georges Brougnard, Definition of GB-sequences.

Index entries for sequences related to 3x+1 (or Collatz) problem

Formula

a(n) = A007918(A138750(n)).

For p prime, a(p) = A138751(A000720(p))

Example

a(7) = 17 since 7 = 1 (mod 3), thus A138750(7) = 2*7 = 14, nextprime(14) = 17.
a(11) = 7 since 11 = 2 (mod 3), thus A138750(11) = ceiling(11/2) = 6, nextprime(6) = 7.

Mathematica

np1[n_]:=Module[{x=Ceiling[n/2]}, If[PrimeQ[x], x, NextPrime[x]]]; np2[n_]:= Module[{x=2n}, If[PrimeQ[x], x, NextPrime[x]]]; Table[If[Mod[n, 3]==2, np1[n], np2[n]], {n, 0, 70}] (* Harvey P. Dale, Jul 10 2013 *)

Prog

(PARI) A138757(n)=nextprime(if(n%3==2, (n+1)\2, 2*n))

Crossrefs

Cf. A124123, A138750, A138751, A138752, A138753, A138754, A138755, A138756, A007918.

Sequence in context: A265988 A340976 A023573 * A158927 A367857 A121258

Adjacent sequences: A138754 A138755 A138756 * A138758 A138759 A138760

Keyword

easy,nonn

Author

M. F. Hasler, Apr 04 2008

Status

approved