A097099 Smallest k>0 such that (2^k)*A002110(n) - 1 is prime.

1, 1, 1, 1, 2, 6, 1, 1, 2, 3, 12, 1, 2, 22, 2, 4, 13, 12, 6, 1, 4, 1, 4, 9, 2, 9, 5, 6, 2, 1, 9, 17, 22, 7, 19, 73, 23, 12, 5, 27, 33, 64, 33, 5, 7, 41, 44, 35, 29, 3, 19, 6, 26, 5, 11, 9, 33, 34, 16, 63, 46, 8, 4, 24, 48, 32, 11, 29, 26, 6, 25, 17, 31, 6, 46, 33, 46, 17, 8, 61, 12, 23, 76

Offset

1,5

Links

Pierre CAMI, Table of n, a(n) for n = 1..1042

Mathematica

f[n_] := Block[{k = 1, p = Product[Prime[i], {i, n}]}, While[ !PrimeQ[2^k*p - 1], k++ ]; k]; Table[ f[n], {n, 83}] (* Robert G. Wilson v, Sep 27 2004 *)
kp[n_]:=Module[{k=1}, While[!PrimeQ[2^k n-1], k++]; k]; With[{prmrls=Rest[ FoldList[Times, 1, Prime[Range[90]]]]}, kp/@prmrls] (* Harvey P. Dale, Feb 01 2012 *)

Prog

(PFGW & SCRIPT)
Command pfgw64 -f in.txt
in.txt file = SCRIPT file
SCRIPT
DIM n, 0
DIM i, 0
DIM pp
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL loop1
SET n, n+1
SET i, 0
LABEL loop2
SET i, i+1
SETS t, %d, %d, %d\,; n; p(n); i
SET pp, (2^i)*p(n)#-1
PRP pp, t
IF ISPRP THEN GOTO a
GOTO loop2
LABEL a
WRITE myf, t
GOTO loop1

Crossrefs

Cf. A002110, A098929.

Sequence in context: A244814 A090185 A059813 * A316622 A197111 A065529

Adjacent sequences: A097096 A097097 A097098 * A097100 A097101 A097102

Keyword

nonn

Author

Pierre CAMI, Sep 15 2004

Extensions

More terms from Robert G. Wilson v, Sep 27 2004

Status

approved