A130327 Least prime p such that 3*p*2^n-1 and 3*p*2^n+1 are twin primes.
2, 2, 5, 3, 5, 2, 11, 3, 19, 17, 5, 113, 59, 317, 331, 307, 241, 2, 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
Offset: 0
Keywords
Examples
3*2*2^0-1=5, 3*2*2^0+1=7: 5 and 7 are twin primes so for n=0 p=2. 3*2*2^1-1=11, 3*2*2^1+1=13: 11 and 13 are twin primes so for n=1 p=2.
Links
- Pierre CAMI, Table of n, a(n) for n = 0..200
Programs
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Mathematica
lpp[n_]:=Module[{p=2},While[!AllTrue[3p 2^n+{1,-1},PrimeQ],p=NextPrime[p]];p]; Array[lpp,60,0] (* Harvey P. Dale, May 13 2022 *) -
PARI
a(n) = my(p=2); while (!(isprime(q=3*p*2^n-1) && isprime(q+2)), p=nextprime(p+1)); p; \\ Michel Marcus, Sep 23 2019