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

Author

Pierre CAMI, Nov 20 2019

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

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