A295013 Prime time primes on 6-digit clocks, second definition: primes of the form HMMSS where H, MM, SS are primes, H < 24, MM and SS < 60.

20219, 20231, 20261, 20297, 20323, 20341, 20347, 20353, 20359, 20389, 20507, 20543, 20707, 20717, 20719, 20731, 20743, 20747, 20753, 20759, 20771, 20773, 20789, 21107, 21143, 21179, 21313, 21317, 21319, 21323, 21341, 21347, 21379, 21383, 21397, 21713

Offset: 1

Author

M. F. Hasler, Jan 09 2018

Keywords

• nonn
• base
• fini
• full

Comments

A subsequence and variant of A229106, where the individual digit groups are not required to be primes. Also a subsequence (namely, the prime terms) of A295014, where H, MM and SS must be primes, but not the concatenation HMMSS.

See A295000 for the subsequence of terms for which the number of seconds after midnight (3600*H + 60*MM + SS, listed in A295003) is also prime.

Links

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

Crossrefs

Cf. A050246, A159911, A229106; A118848, A118849, A118850.

Cf. A295014, A295003, A295011, A295000, A295002.

Programs

Mathematica

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

PARI

is_A295013(n)=apply(isprime,digits(n,100))==[1,1,1]&&n<24e4&&isprime(n)
A295013 = select( is_A295013, primes([20000,240000]))