A073741 Number of steps needed to reach a prime when the following map is repeatedly applied to n: if n is even then 2n+1, otherwise 2n-1; or -1 if no prime is ever reached.

1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 3, 3, 1, 1, 4, 4, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 3, 3, 2, 2, 1, 1, 5, 5, 4, 4, 3, 3, 1, 1, 8, 8, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 2, 2, 2, 2, 7, 7, 2, 2, 5, 5, 1, 1, 2, 2, 3, 3, 1, 1, 4, 4, 1, 1, 3, 3, 10, 10, 2, 2, 1, 1, 2, 2, 1, 1, 7, 7, 582, 582, 1, 1, 1, 1, 2, 2, 2, 2

Offset

2,3

Links

Table of n, a(n) for n=2..103.

Example

For n=4, a(4)=2 because 4 ->9 ->17

Mathematica

pr[n_]:=Module[{c=If[EvenQ[n], 2n+1, 2n-1]}, Length[NestWhileList[ If[EvenQ[#], 2#+1, 2#-1]&, c, !PrimeQ[#]&]]]; Array[pr, 102, 2] (* Harvey P. Dale, Oct 05 2012 *)

Prog

(UBASIC) 10 cls 30 for I=2 to 100 32 H=I 40 if odd(H)=1 then goto 90 else goto 50 50 A=2*H+1:K=K+1 60 if prmdiv(A)=A then print I, K:goto 120 65 if K>10000 then print I, "no solution":goto 120 70 H=A:goto 40 90 A=2*H-1:K=K+1 100 if prmdiv(A)=A then print I, K:goto 120 105 if K>10000 then print I, "no solution":goto 120 110 H=A:goto 40 120 K=0 130 next

Crossrefs

Sequence in context: A328581 A238643 A140193 * A071838 A157896 A358469

Adjacent sequences: A073738 A073739 A073740 * A073742 A073743 A073744

Keyword

easy,nonn

Author

Felice Russo, Sep 02 2002

Extensions

More terms from Jason Earls, Sep 04 2002

Status

approved