A050246 -id:A050246 - cp's OEIS frontend

A295003 The number of seconds after midnight corresponding to prime time primes, i.e., primes of the form HMMSS with primes H < 24 and MM, SS < 60, cf. A295013.

7339, 7351, 7381, 7417, 7403, 7421, 7427, 7433, 7439, 7469, 7507, 7543, 7627, 7637, 7639, 7651, 7663, 7667, 7673, 7679, 7691, 7693, 7709, 7867, 7903, 7939, 7993, 7997, 7999, 8003, 8021, 8027, 8059, 8063, 8077, 8233, 8257, 8287, 8293, 8351, 8369, 8377, 8383

Offset: 1

M. F. Hasler, Jan 15 2018

See A295002 for the primes within this sequence, and A295000 for the corresponding 6-digit clock times.

M. F. Hasler, Table of n, a(n) for n = 1..1211 (complete sequence).

Cf. A295013, A295002, A295000, A295014, A295011; A050246, A159911, A229106; A118848, A118849, A118850.

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

apply( A292579, A295013) \\ convert prime time primes to seconds

A295004 The number of seconds after midnight (3600H + 60MM + SS) corresponding to prime time numbers A295014, i.e., numbers of the form HMMSS with primes H < 24 and MM, SS < 60.

Original entry on oeis.org

7322, 7323, 7325, 7327, 7331, 7333, 7337, 7339, 7343, 7349, 7351, 7357, 7361, 7363, 7367, 7373, 7379, 7382, 7383, 7385, 7387, 7391, 7393, 7397, 7399, 7403, 7409, 7411, 7417, 7421, 7423, 7427, 7433, 7439, 7502, 7503, 7505, 7507, 7511, 7513, 7517, 7519, 7523

Offset: 1

M. F. Hasler, Jan 15 2018

See A295003 for the subsequence of terms which correspond to "prime time primes" (cf. A295013), and A295002 for the primes among these.

This is to A295014 what is A295003 to A295013, or what is A118848 to A050246, or what is A118850 to A118849.

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

Cf. A295014, A295003, A295013, A295011, A295002, A295000; A050246, A159911, A229106; A118848, A118849, A118850.

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

apply( A292579, A295014) \\ convert prime time numbers to seconds

a(n) = A292579(A295014(n))

A129336 Digital clock semiprimes.

Original entry on oeis.org

4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 201, 202, 203, 205, 206, 209, 213, 214, 215, 217, 218, 219, 221, 226, 235, 237, 247

Offset: 1

Jonathan Vos Post, May 27 2007

Semiprime analog of A050246. Semiprimes possible on a 24-hour digital clock, with no seconds. The largest value is a(414) = 2359 = 7 * 337 because 23:59 is the largest 4-digit number that appears on a 24-hour digital clock.

			253 is in the sequence because (see the comic) a character looks at a digital clock reading 2:53 and says: "253 is 11 x 23." That clock-time is a semiprime.

Nathaniel Johnston, Table of n, a(n) for n = 1..414 (full sequence)
Randall Munroe, Factoring the Time
Eric Weisstein's World of Mathematics, Clock Prime

Cf. A001358, A050246, A118848, A118849, A118850.

with(numtheory): for h from 0 to 23 do for m from 0 to 59 do t:=100*h+m: if(bigomega(t)=2)then printf("%d, ",t): fi: od: od: # Nathaniel Johnston, May 17 2011

A316603 Double prime times.

Original entry on oeis.org

13, 17, 23, 29, 31, 37, 59, 101, 103, 107, 127, 223, 227, 229, 233, 239, 251, 311, 331, 349, 353, 359, 401, 409, 419, 421, 457, 509, 521, 523, 541, 547, 601, 631, 647, 701, 733, 751, 811, 827, 829, 839, 853, 911, 929, 937, 941, 953, 1013, 1021, 1039, 1051, 1109, 1151, 1213

Offset: 1

Hugo Pfoertner, Jul 15 2018

Numbers on the display of a 4-digit hh:mm digital clock that remain prime when the display mode is switched between 12-hour AM/PM and 24-hour time.

			a(49) = 1013 and a(103) = 2213 are in the sequence, because toggling the display mode of the digital clock will either leave 10:13 unchanged or switch between 22:13 and 10:13 at 10:13 PM. Both displayed times are prime when reading hh:mm as decimal number.

Hugo Pfoertner, Table of n, a(n) for n = 1..108
Forums for the webcomic xkcd.com, 0247: "Factoring the Time", post by user jasticE, Apr 12 2007.
Randall Munroe, Factoring the time, xkcd Web Comic #247, Apr 11 2007.

Cf. A050246.

apd(x)=2400*((x>1200)-1/2);
for(h=0,23,for(m=0,59,t=100*h+m;t12=t-apd(t);if(isprime(t)&&isprime(t12),print1(t,", ")))) \\ Hugo Pfoertner, Jul 18 2018

A229107 Palindromic prime time display in hours, minutes, seconds on a six-digit 24-hour digital clock.

Original entry on oeis.org

2, 3, 5, 7, 11, 101, 131, 151, 313, 353, 727, 757, 919, 929, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741, 15451, 15551, 30103, 30203, 30403, 30703, 30803, 31013, 31513, 32323, 32423, 33533, 34543, 34843, 35053

Offset: 1

Shyam Sunder Gupta, Sep 13 2013

Leading zeros are ignored, so the term a(7) = 131, for example, corresponds to the display 00:01:31. Sequence has 69 entries.

			151 is in the sequence because it is palindromic prime and displays the time as 00:01:51.

Shyam Sunder Gupta, Table of n, a(n) for n = 1..69 (complete sequence)

Cf. A222620, A050246.

palindromicQ[n_] := TrueQ[IntegerDigits[n] == Reverse[IntegerDigits[n]]]; Select[Select[Table[10000 hr + 100 mnt + sec, {hr, 0, 23}, {mnt, 0, 59}, {sec, 0, 59}] // Flatten, palindromicQ@# &], PrimeQ]

A234631 Timestamps Hmmss where H,mm,ss are three consecutive primes, 0 < H < 24.

Original entry on oeis.org

20305, 30507, 50711, 71113, 111317, 131719, 171923, 192329, 232931

Offset: 1

M. F. Hasler, Dec 28 2013

			The terms correspond to the following timestamps:
    02:03:05
    03:05:07
    05:07:11
    07:11:13
    11:13:17
    13:17:19
    17:19:23
    19:23:29
    23:29:31

A. Kulsha, Re: The probability of occurrence of 3 consecutive primes, primenumbers group, Dec 28 2013.
A. Kulsha, Re: The probability of occurrence of 3 consecutive primes [Cached copy]

Cf. A050246, A316603.

forprime(h=1,24,printf("%d%02d%02d, ",h,m=nextprime(h+1),nextprime(m+1)))

cp's OEIS Frontend

A295003 The number of seconds after midnight corresponding to prime time primes, i.e., primes of the form HMMSS with primes H < 24 and MM, SS < 60, cf. A295013.

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A295004 The number of seconds after midnight (3600*H + 60*MM + SS) corresponding to prime time numbers A295014, i.e., numbers of the form HMMSS with primes H < 24 and MM, SS < 60.

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Formula

A129336 Digital clock semiprimes.

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Maple

A316603 Double prime times.

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PARI

A229107 Palindromic prime time display in hours, minutes, seconds on a six-digit 24-hour digital clock.

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Mathematica

A234631 Timestamps Hmmss where H,mm,ss are three consecutive primes, 0 < H < 24.

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Author

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Programs

PARI

A295004 The number of seconds after midnight (3600H + 60MM + SS) corresponding to prime time numbers A295014, i.e., numbers of the form HMMSS with primes H < 24 and MM, SS < 60.