A249806 Smallest odd number k>1 such that k*2^prime(n)-1 is also prime.

3, 3, 7, 3, 3, 9, 7, 51, 13, 7, 15, 21, 15, 3, 31, 147, 45, 69, 43, 73, 15, 69, 91, 19, 51, 81, 3, 25, 9, 85, 103, 55, 169, 225, 109, 145, 15, 103, 615, 69, 259, 69, 63, 45, 285, 471, 9, 255, 169, 489, 69, 273, 427, 43, 391, 169, 201, 21

Offset

1,1

Comments

If prime(n) is a Mersenne prime exponent then 2^prime(n)-1 is a prime < k*2^prime(n)-1.

Links

Pierre CAMI, Table of n, a(n) for n = 1..1000

Maple

3*2^2-1=11 prime so a(1)=3.
3*2^3-1=23 prime so a(2)=3.
3*2^5-1=95 composite, 5*2^5-1=159 composite, 7*2^5-1=223 prime so a(3)=7.

Mathematica

a249806[n_Integer] := Catch[Module[{k}, For[k = 3, k < 10^5, k += 2, If[PrimeQ[k*2^Prime[n] - 1], Throw[k], 0]]]]; a249806 /@ Range[120] (* Michael De Vlieger, Nov 11 2014 *)

Prog

(PFGW & SCRIPT)
SCRIPT
DIM j, 0
DIM k
DIM n
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL loop1
SET j, j+1
IF j>1000 THEN END
SET k, p(j)
SET n, 1
LABEL loop2
SET n, n+2
SETS t, %d, %d, %d\,; j; k; n
PRP n*2^k-1, t
IF ISPRP THEN GOTO a
GOTO loop2
LABEL a
WRITE myf, t
GOTO loop1
(PARI) s=[]; forprime(p=2, 500, k=3; q=2^p; while(!ispseudoprime(k*q-1), k+=2); s=concat(s, k)); s \\ Colin Barker, Nov 06 2014

Crossrefs

Cf. A135434.

Sequence in context: A076560 A359048 A096915 * A249382 A317929 A285387

Adjacent sequences: A249803 A249804 A249805 * A249807 A249808 A249809

Keyword

nonn

Author

Pierre CAMI, Nov 06 2014

Status

approved