A329916 Smallest k such that 6*k*A057130(n)-1 and 6*k*A057130(n)+1 are twin primes.

1, 2, 3, 23, 11, 18, 77, 46, 84, 76, 22, 30, 3, 107, 26, 198, 136, 23, 236, 284, 167, 269, 381, 405, 379, 374, 620, 481, 606, 505, 163, 1414, 348, 639, 1696, 1429, 850, 2050, 740, 117, 362, 35, 3961, 72, 1307, 1816, 9410, 5705, 972, 368, 5083, 4387, 3296, 6039

Offset

1,2

Comments

A057130 gives the product of prime numbers (-1 mod 6) in the order of occurrence.

Links

Table of n, a(n) for n=1..54.

Example

A057130(1)=5, 6*1*5-1=29, and 29 and 31 are twin primes, so a(1)=1.
A057130(2)=55, 6*2*55-1=659, and 659 and 661 are twin primes, so a(2)=2.

Prog

(PFGW Script)
SCRIPT
DIM i, 0
DIM j
DIM k
DIM n, 1
OPENFILEOUT myf, a(n).txt
OPENFILEIN maf, a007528.txt
LABEL a
SET i, i+1
IF i>100 THEN END
GETNEXT j, maf
SET n, n*j
SET k, 0
LABEL b
SET k, k+1
PRP k*6+1, k
IF ISPRP THEN GOTO c
GOTO b
LABEL c
PRP k*6*n-1, k
IF ISPRP THEN GOTO d
GOTO b
LABEL d
WRITE myf, k
GOTO a
(PARI) lista(nn) = {my(pp = 1); forprime (p = 1, nn, if (Mod(p, 6) == -1, pp *= p; my(k=1); while (!isprime(6*k*pp-1) || !isprime(6*k*pp+1), k++); print1(k, ", "); ); ); } \\ Michel Marcus, Nov 25 2019

Crossrefs

Cf. A001359, A006512, A007528, A057130, A060256, A173937, A329736.

Sequence in context: A114007 A282795 A071819 * A085946 A280894 A042585

Adjacent sequences: A329913 A329914 A329915 * A329917 A329918 A329919

Keyword

nonn

Author

Pierre CAMI, Nov 24 2019

Status

approved