A316603 - OEIS

%I #15 Jul 18 2018 04:12:33

%S 13,17,23,29,31,37,59,101,103,107,127,223,227,229,233,239,251,311,331,

%T 349,353,359,401,409,419,421,457,509,521,523,541,547,601,631,647,701,

%U 733,751,811,827,829,839,853,911,929,937,941,953,1013,1021,1039,1051,1109,1151,1213

%N Double prime times.

%C 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.

%H Hugo Pfoertner, <a href="/A316603/b316603.txt">Table of n, a(n) for n = 1..108</a>

%H Forums for the webcomic xkcd.com, <a href="http://forums.xkcd.com/viewtopic.php?f=7&amp;t=4051&amp;start=78">0247: "Factoring the Time"</a>, post by user jasticE, Apr 12 2007.

%H Randall Munroe, <a href="https://xkcd.com/247/">Factoring the time</a>, xkcd Web Comic #247, Apr 11 2007.

%e 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.

%o (PARI) apd(x)=2400*((x>1200)-1/2);

%o 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

%Y Cf. A050246.

%K nonn,base,easy,fini,full

%O 1,1

%A _Hugo Pfoertner_, Jul 15 2018