A224490 Smallest k such that k*2*p(n)^2-1=q is prime and k*2*q^2-1 is also prime.

1, 1, 25, 9, 21, 3, 1, 16, 25, 136, 10, 33, 90, 250, 10, 55, 1, 9, 36, 75, 1, 4, 33, 406, 103, 15, 121, 4, 244, 78, 28, 19, 49, 105, 45, 34, 10, 46, 33, 4, 111, 15, 9, 36, 118, 66, 10, 13, 31, 76, 66, 36, 55, 15, 4, 48, 6, 66, 13, 34, 54, 64, 153, 1, 60, 48

Offset

1,3

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

1*2*2^2-1=7 prime q 1*2*7^2-1=97 also prime so a(1)=1.

Mathematica

a[n_] := For[k = 1, True, k++, p = Prime[n]; If[PrimeQ[q = k*2*p^2 - 1] && PrimeQ[k*2*q^2 - 1], Return[k]]]; Table[a[n], {n, 1, 66}] (* Jean-François Alcover, Apr 12 2013 *)

Prog

SCRIPT
DIM k
DIM i, 0
DIM q
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL a
SET i, i+1
IF i>20000 THEN END
SET k, 0
LABEL b
SET k, k+1
SETS t, %d, %d, %d\,; k; i; p(i)
SET q, k*2*p(i)^2-1
PRP q, t
IF ISPRP THEN GOTO c
GOTO b
LABEL c
SET q, k*2*q^2-1
PRP q, t
IF ISPRP THEN WRITE myf, t
IF ISPRP THEN GOTO a
GOTO b

Crossrefs

Cf. A224489, A224491, A224492.

Sequence in context: A065910 A096521 A215539 * A226224 A181763 A171638

Adjacent sequences: A224487 A224488 A224489 * A224491 A224492 A224493

Keyword

nonn

Author

Pierre CAMI, Apr 08 2013

Extensions

Typo in name fixed by Zak Seidov, Apr 11 2013

Status

approved