A212956 Least k such that k*30^n-1 , k*30^n+1, and 2*k*30^n-1 are prime; that is, twin primes and a Sophie Germain prime.

1, 13, 91, 209, 213, 217, 8, 283, 82, 3150, 105, 3729, 3548, 1267, 5218, 3459, 571, 1911, 12088, 858, 4606, 3171, 5305, 6890, 5024, 19149, 14766, 16640, 15333, 39382, 8692, 49314, 53630, 123600, 4120, 57993, 47136, 20530, 115743, 30022, 31457, 76736, 25842

Offset

1,2

Links

Pierre CAMI, Table of n, a(n) for n = 1..125

Example

1*30^1-1 = 29, 1*30^1+1 = 31, 2*1*30^1-1 = 59. Because 29, 31, and 59 are prime, a(1) = 1.

Mathematica

Table[k = 1; While[! PrimeQ[k*30^n + 1] || ! PrimeQ[k*30^n - 1] || ! PrimeQ[2 k*30^n - 1], k++]; k, {n, 50}] (* T. D. Noe, Jun 01 2012 *)

Prog

PFGW64 and SCRIPTIFY from Primeform Group
command: pfgw64 -f in.txt
in.txt file :
SCRIPT
DIM nn, 0
DIM kk, 0
DIMS tt
OPENFILEOUT myfil, b(n).txt
LABEL loopn
SET nn, nn+1
IF nn>125 THEN END
SET kk, 0
LABEL loopk
SET kk, kk+1
SETS tt, %d, %d\,; nn; kk
PRP kk*30^nn-1, tt
IF ISPRP THEN GOTO a
IF ISPRIME THEN GOTO a
GOTO loopk
LABEL a
PRP kk*30^nn+1, tt
IF ISPRP THEN GOTO b
IF ISPRIME THEN GOTO b
GOTO loopk
LABEL b
PRP 2*kk*30^nn-1, tt
IF ISPRP THEN GOTO c
IF ISPRIME THEN GOTO c
GOTO loopk
LABEL c
WRITE myfil, tt
GOTO loopn

Crossrefs

Cf. A212955.

Sequence in context: A131700 A156947 A139613 * A188352 A162631 A247611

Adjacent sequences: A212953 A212954 A212955 * A212957 A212958 A212959

Keyword

nonn

Author

Pierre CAMI, Jun 01 2012

Status

approved