A295011 Numbers of the form HMMSS with primes H < 24 and MM, SS < 60, for which the number of seconds after midnight, 3600*H+60*MM+SS, is also prime.

20211, 20213, 20229, 20231, 20313, 20331, 20337, 20353, 20507, 20517, 20523, 20529, 20537, 20541, 20547, 20559, 20719, 20723, 20729, 20753, 21107, 21113, 21117, 21119, 21123, 21141, 21147, 21159, 21313, 21329, 21331, 21337, 21359, 21711, 21713, 21717

Offset: 1

Author

M. F. Hasler, Jan 16 2018

Keywords

• nonn
• base
• fini
• full

Comments

Subsequence of A295014 (prime time numbers) for which the corresponding number of seconds after midnight (A295004) is also prime.

The "super prime time primes" A295000 are the primes within this sequence.

Examples

			Construct all numbers of the form concat(H,MM,SS) where H < 24 and MM, SS < 60 are primes. These start 2:02:02, 2:02:03, 2:02:03, ... (without ":"s), this is A295014. The corresponding number of seconds after midnight is A292579(HMMSS) = 3600*H + 60*MM + SS. These numbers are listed in A295004. The first prime in that sequence is 7331 = A292579(20211), i.e., the first H:MM:SS for which that number of seconds is prime is 2:02:11, whence a(1) = 20211.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..770 (complete sequence).

Crossrefs

Cf. A295014, A295004, A295000, A295002, A295013, A295003; A050246, A159911, A229106; A118848, A118849, A118850.

Programs

Mathematica

With[{s = Prime@ Range@ PrimePi@ 60}, FromDigits@ Flatten[PadLeft[IntegerDigits[#], 2] & /@ #] & /@ Select[Tuples@ {TakeWhile[s, # < 24 &], s, s}, PrimeQ@ NumberCompose[{#1, #2, #3}, {3600, 60, 1}] & @@ # &]] (* Michael De Vlieger, Jan 21 2018 *)

PARI

select( t->isprime(A292579(t)), A295014)