

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.


7



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
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OFFSET

1,1


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.


LINKS

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


EXAMPLE

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.


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 *)


PROG

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


CROSSREFS

Cf. A295014, A295004, A295000, A295002, A295013, A295003; A050246, A159911, A229106; A118848, A118849, A118850.
Sequence in context: A053073 A295014 A133527 * A146961 A295013 A295000
Adjacent sequences: A295008 A295009 A295010 * A295012 A295013 A295014


KEYWORD

nonn,base,fini,full


AUTHOR

M. F. Hasler, Jan 16 2018


STATUS

approved



