A329736 Smallest odd prime P such that P*3*2^n - 1 and P*3*2^n + 1 are twin primes.

3, 5, 3, 5, 43, 11, 3, 19, 17, 5, 113, 59, 317, 331, 307, 241, 127, 829, 23, 149, 127, 11, 3023, 1091, 787, 971, 1523, 2741, 727, 1051, 227, 211, 727, 89, 1163, 71, 367, 1031, 577, 89, 1213, 1151, 3, 1021, 283, 2699, 4933, 59, 647, 709, 3083, 541, 1483, 2069

Offset

1,1

Links

Daniel Starodubtsev, Table of n, a(n) for n = 1..1000

Example

3*3*2^1 - 1 =  17,  17 and  19 are twin primes so a(1)=3.
5*3*2^2 - 1 =  59,  59 and  61 are twin primes so a(2)=5.
3*3*2^3 - 1 =  71,  71 and  73 are twin primes so a(3)=3.
5*3*2^4 - 1 = 119, 119 and 121 are twin primes so a(4)=5.

Mathematica

Array[Block[{p = 3}, While[! AllTrue[3 p*2^# + {-1, 1}, PrimeQ], p = NextPrime@ p]; p] &, 54] (* Michael De Vlieger, Nov 21 2019 *)

Prog

(PFGW Script)
SCRIPT
DIM i
DIM j
DIM n, 0
OPENFILEOUT myf, a(n).txt
LABEL loop1
SET n, n+1
IF n>500 THEN END
SET i, 1
LABEL loop2
SET i, i+1
SET j, p(i)
PRP j*3*2^n-1, n
IF ISPRP THEN GOTO a
GOTO loop2
LABEL a
PRP j*3*2^n+1, n
IF ISPRP THEN GOTO b
GOTO loop2
LABEL b
WRITE myf, j
GOTO loop1
(PARI) for(n=1, 54, my(m=3*2^n); forprime(k=3, oo, my(j=k*m); if(ispseudoprime(j-1)&&ispseudoprime(j+1), print1(k, ", "); break))) \\ Hugo Pfoertner, Nov 21 2019
(PARI) a(n) = my(p=3, q); while (!isprime(q=p*3*2^n - 1) || !isprime(q+2), p = nextprime(p+1)); p; \\ Michel Marcus, May 06 2020

Crossrefs

Cf. A001359, A006512, A013597, A051886, A173937, A210651.

Sequence in context: A151568 A134429 A100667 * A324086 A286108 A096438

Adjacent sequences: A329733 A329734 A329735 * A329737 A329738 A329739

Keyword

nonn

Author

Pierre CAMI, Nov 20 2019

Status

approved