A295004 -id:A295004 - 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.

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

M. F. Hasler, Jan 15 2018

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.

			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.

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

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

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

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

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

Original entry on oeis.org

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

M. F. Hasler, Jan 16 2018

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.

			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.

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

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

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 *)

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

A295014 Prime time numbers on 6-digit clocks: numbers of the form HMMSS where H, MM, SS are primes, H < 24, MM and SS < 60.

Original entry on oeis.org

20202, 20203, 20205, 20207, 20211, 20213, 20217, 20219, 20223, 20229, 20231, 20237, 20241, 20243, 20247, 20253, 20259, 20302, 20303, 20305, 20307, 20311, 20313, 20317, 20319, 20323, 20329, 20331, 20337, 20341, 20343, 20347, 20353, 20359, 20502, 20503

Offset: 1

M. F. Hasler, Jan 09 2018

The primes in this sequence form the subsequence A295013, a variant and subsequence of A229106, where only the concatenation HMMSS but not the individual digit groups are required to be primes. See also A050246 and A159911 for 4-digit clock variants.

See A295011 for the subsequence of terms for which the number of seconds after midnight (3600*H + 60*MM + SS, given in A295004) is prime, and A295000 for the subsequence of primes therein.

M. F. Hasler, Table of n, a(n) for n = 1..2601 (complete sequence).

Cf. A295013, A050246, A159911, A229106.

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

is_A295014(n)=apply(isprime,digits(n,100))==[1,1,1]&&n<24e4
A295014 = select( is_A295014, [20000,240000])
/* alternatively */ A295014=List(); forprime(h=0,24,forprime(m=0,60,forprime(s=0,60,listput(A295014,(h*100+m)*100+s))))

A295002 Primes in A295003, the number of seconds after midnight corresponding to prime time primes A295013 (primes of the form HMMSS with primes H < 24 and MM, SS < 60).

Original entry on oeis.org

7351, 7417, 7433, 7507, 7639, 7673, 7691, 7867, 7993, 8059, 8233, 8287, 8293, 8369, 8377, 8623, 8647, 8677, 9001, 9013, 9091, 9103, 9127, 9133, 9157, 9439, 9461, 9463, 9467, 9473, 9697, 9739, 9817, 9839, 9851, 9859, 10453, 10753, 10771, 10837, 10867, 10949

Offset: 1

M. F. Hasler, Jan 15 2018

See A295000(n) = A055643(a(n)) for the corresponding "prime time primes", i.e., 6-digit clock displays. Reciprocally, the number of seconds given here is obtained through A292579 from the "super prime time primes" A295000.

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

Cf. A295000, A295003, A295013, A295011, A295014, A295004; A050246, A159911, A229106; A118848, A118849, A118850.

select( isprime, A295003) /* or */ apply(A292579,A295000)

a(n) = A292579(A295000(n))

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.

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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.

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A295014 Prime time numbers on 6-digit clocks: numbers of the form HMMSS where H, MM, SS are primes, H < 24, MM and SS < 60.

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A295002 Primes in A295003, the number of seconds after midnight corresponding to prime time primes A295013 (primes of the form HMMSS with primes H < 24 and MM, SS < 60).

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