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.

20231, 20297, 20353, 20507, 20719, 20753, 20771, 21107, 21313, 21379, 21713, 21767, 21773, 21929, 21937, 22343, 22367, 22397, 22961, 22973, 23131, 23143, 23167, 23173, 23197, 23719, 23741, 23743, 23747, 23753, 24137, 24179, 24337, 24359, 24371, 24379

Offset

1,1

Comments

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.

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.

Sequence A295002 lists the number of seconds after midnight corresponding to the "prime times" = 6-digit clock displays listed here.

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.

Links

M. F. Hasler, Table of n, a(n) for n = 1..404 (complete sequence).

Formula

a(n) = A055643(A295002(n)) ; A295000 = { A295013(k) | A295003(k) is prime }.

Example

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.

Prog

(PARI) apply( A055643, A295002) /* or */ select( p->isprime(A292579(p)), A295013)

Crossrefs

Cf. A295002, A295003, A295013, A295011, A295004, A295014; A050246, A159911, A229106; A118848, A118849, A118850; A055643, A292579.

Sequence in context: A295011 A146961 A295013 * A250451 A031825 A234631

Adjacent sequences: A294997 A294998 A294999 * A295001 A295002 A295003

Keyword

nonn,base,fini,full

Author

M. F. Hasler, Jan 15 2018

Status

approved