|
%I #33 Sep 24 2023 10:41:36
%S 1,1,7,24,12,52,24,39,252,112,371,184,5772,44649,61939,151505,64125,
%T 533040,407635,273249,3901012,718187,3527063,9522163,23128315,
%U 20121642,337342290,388787370
%N a(n) is the least K such that K*6*M(n) - 1 and K*6*M(n) + 1 are twin primes, where M(n) = n-th Mersenne prime.
%H R. Gerbicz, <a href="https://primes.utm.edu/bios/page.php?id=3934">PolySieve program at UTM Prime Pages</a>.
%H Mersenneforum, <a href="https://mersenneforum.org/showthread.php?t=24167">k.Mp +/- 1 discussion thread</a>.
%e 7*6*(2^5-1)-1=1301 prime, 1301 and 1303 twin primes so K(3)=7 as M(3)=2^5-1.
%t Array[Block[{k = 1, m = 2^MersennePrimeExponent@ # - 1}, While[! AllTrue[6 k m + {-1, 1}, PrimeQ], k++]; k] &, 14] (* _Michael De Vlieger_, Dec 22 2019 *)
%o (PARI) forprime(p=2,607,if(isprime(Mp=2^p-1),forstep(k=6,10^9,6,if(isprime(k*Mp-1),if(isprime(k*Mp+1),print1(k/6", ");break))))) \\ _Serge Batalov_, Dec 22 2019
%Y Cf. A000043, A000668.
%K nonn,more
%O 1,3
%A _Pierre CAMI_, Feb 08 2007
%E Missing term 44649 and a(26-28) from _Serge Batalov_, Dec 21 2019
|
