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.

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

Author

M. F. Hasler, Jan 09 2018

Keywords

• nonn
• base
• fini
• full

Comments

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.

Links

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

Crossrefs

Cf. A295013, A050246, A159911, A229106.

Programs

Mathematica

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

PARI

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))))