cp's OEIS Frontend

A295000 Prime time primes (of the form HMMSS with primes H < 24 and MM, SS < 60) such that the corresponding number of seconds after midnight is also prime.

%I A295000 #24 Jan 16 2018 08:51:13
%S A295000 20231,20297,20353,20507,20719,20753,20771,21107,21313,21379,21713,
%T A295000 21767,21773,21929,21937,22343,22367,22397,22961,22973,23131,23143,
%U A295000 23167,23173,23197,23719,23741,23743,23747,23753,24137,24179,24337,24359,24371,24379
%N A295000 Prime time primes (of the form HMMSS with primes H < 24 and MM, SS < 60) such that the corresponding number of seconds after midnight is also prime.
%C A295000 Could be called "super prime time primes": all of H, MM, SS, HMMSS (6-digit clock display) and H*3600 + MM*60 + SS (seconds after midnight) are prime.
%C A295000 This sequence lists the prime time primes A295013 for which the number of seconds A295003 is prime. These are also the times HMMSS (obtained through A055643) which correspond to the subset A295002 of primes in A295003.
%C A295000 Sequence A295002 lists the number of seconds after midnight corresponding to the "prime times" = 6-digit clock displays listed here.
%C A295000 Sequences A295003 and A295004 list the number of seconds after midnight corresponding to the prime time primes A295013 and prime time numbers A295014, i.e., primes and all numbers of the form HMMSS where H < 24 and MM, SS < 60 are prime.
%H A295000 M. F. Hasler, <a href="/A295000/b295000.txt">Table of n, a(n) for n = 1..404</a> (complete sequence).
%F A295000 a(n) = A055643(A295002(n)) ; A295000 = { A295013(k) | A295003(k) is prime }.
%e A295000 The smallest prime of the form HMMSS, with H, MM, SS and H*3600 + MM*60 + SS also prime, is a(1) = 20231, corresponding to a prime number A295002(1) = H*3600 + MM*60 + SS = 7351 (the first prime in A295003) of seconds after midnight.
%o A295000 (PARI) apply( A055643, A295002) /* or */ select( p->isprime(A292579(p)), A295013)
%Y A295000 Cf. A295002, A295003, A295013, A295011, A295004, A295014; A050246, A159911, A229106; A118848, A118849, A118850; A055643, A292579.
%K A295000 nonn,base,fini,full
%O A295000 1,1
%A A295000 _M. F. Hasler_, Jan 15 2018