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Primes p such that p, p+12, p+24 are consecutive primes.
13

%I #32 Sep 08 2022 08:44:59

%S 199,1499,4397,4679,7829,9859,11287,11399,11719,12829,15149,16607,

%T 17419,17839,18329,18719,19727,19937,20149,20509,20719,21649,22039,

%U 22247,23789,25609,26029,28057,29587,30047,31039,32467,34159,35117

%N Primes p such that p, p+12, p+24 are consecutive primes.

%C Corresponds to two consecutive 12's in A001223. - - _M. F. Hasler_, Jan 02 2020

%H Zak Seidov, <a href="/A052188/b052188.txt">Table of n, a(n) for n = 1..1000</a>

%H OEIS wiki, <a href="/wiki/Consecutive_primes_in_arithmetic_progression#CPAP_with_given_gap">Consecutive primes in arithmetic progression: CPAP with given gap</a>, updated Jan. 2020

%e a(1)=199, followed by 199+12=211, 199+12+12=223 consecutive primes.

%t Transpose[Select[Partition[Prime[Range[3800]],3,1], Union[Differences[#]] =={12}&]][[1]] (* _Harvey P. Dale_, Apr 26 2011 *)

%o (PARI) lista(nn) = {forprime(p=1, nn, q = nextprime(p+1); r = nextprime(q+1); if ((r-q==12) && (q-p==12), print1(p, ", ")););} \\ _Michel Marcus_, Jun 27 2015

%o (Magma) [p:p in PrimesUpTo(36000)| NextPrime(p)-p eq 12 and NextPrime(p+12)-p eq 24]; // _Marius A. Burtea_, Jan 03 2020

%Y Generalization of A047948 and A033451 if 6 replaced by 12. Cf. A033447.

%K nonn

%O 1,1

%A _Labos Elemer_, Jan 28 2000

%E Name changed by _Jon E. Schoenfield_, May 30 2018