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%I #14 Jan 30 2018 21:11:41
%S 20211,20213,20229,20231,20313,20331,20337,20353,20507,20517,20523,
%T 20529,20537,20541,20547,20559,20719,20723,20729,20753,21107,21113,
%U 21117,21119,21123,21141,21147,21159,21313,21329,21331,21337,21359,21711,21713,21717
%N 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.
%C Subsequence of A295014 (prime time numbers) for which the corresponding number of seconds after midnight (A295004) is also prime.
%C The "super prime time primes" A295000 are the primes within this sequence.
%H M. F. Hasler, <a href="/A295011/b295011.txt">Table of n, a(n) for n = 1..770</a> (complete sequence).
%e 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.
%t 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 *)
%o (PARI) select( t->isprime(A292579(t)), A295014)
%Y Cf. A295014, A295004, A295000, A295002, A295013, A295003; A050246, A159911, A229106; A118848, A118849, A118850.
%K nonn,base,fini,full
%O 1,1
%A _M. F. Hasler_, Jan 16 2018
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