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A295014
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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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7
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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
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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With[{s = Prime@ Range@ PrimePi@ 60}, FromDigits@ Flatten[PadLeft[IntegerDigits[#], 2] & /@ #] & /@ Tuples@ {TakeWhile[s, # < 24 &], s, s}] (* Michael De Vlieger, Jan 21 2018 *)
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PROG
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(PARI) is_A295014(n)=apply(isprime, digits(n, 100))==[1, 1, 1]&&n<24e4
/* alternatively */ A295014=List(); forprime(h=0, 24, forprime(m=0, 60, forprime(s=0, 60, listput(A295014, (h*100+m)*100+s))))
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CROSSREFS
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KEYWORD
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nonn,base,fini,full
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AUTHOR
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STATUS
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approved
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