|
%I #17 Mar 04 2024 13:38:26
%S 47,131,331,557,571,941,977,1181,1187,1621,1741,2677,3691,3761,4561,
%T 4951,5407,5521,5807,5861,6037,6317,6337,6977,7481,7541,7681,8081,
%U 8887,10847,11897,12511,12541,12547,12577,13591,14717,15227,15271,15761,15767,19231,19441,22031,22901,23167,25111,25147
%N Primes p such that p and p+6 are consecutive primes, and p+36 and p+42 are consecutive primes.
%C Intersection of A031924 and its translate by -36.
%H Robert Israel, <a href="/A350863/b350863.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 331 is a term because 331 and 331+6 = 337 are consecutive primes and 331+36 = 367 and 331+42 = 373 are consecutive primes.
%p P:= {seq(ithprime(i),i=1..3000)}:
%p R:= P intersect map(`-`, P, 6) intersect map(`-`,P,36) intersect map(`-`,P,42) minus map(`-`,P, 2) minus map(`-`,P,4) minus map(`-`,P,38) minus map(`-`,P,40):
%p sort(convert(R,list));
%t Select[Range[25000], And @@ PrimeQ[(ps = # + {0, 36})] && NextPrime[ps] == ps + {6, 6} &] (* _Amiram Eldar_, Jan 20 2022 *)
%t Select[Select[Partition[Prime[Range[3000]],2,1],#[[2]]-#[[1]]==6&][[;;,1]],PrimeQ[#+36]&& NextPrime[ #+36] ==#+42&] (* _Harvey P. Dale_, Mar 04 2024 *)
%Y Cf. A031924.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Jan 19 2022
|
