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A133794 Times on a 12-hour digital clock with all digits in {1, 2, 3, 4, 5, 6}.

%I A133794 #14 Mar 13 2023 16:41:49
%S A133794 111,112,113,114,115,116,121,122,123,124,125,126,131,132,133,134,135,
%T A133794 136,141,142,143,144,145,146,151,152,153,154,155,156,211,212,213,214,
%U A133794 215,216,221,222,223,224,225,226,231,232,233,234,235,236,241,242,243
%N A133794 Times on a 12-hour digital clock with all digits in {1, 2, 3, 4, 5, 6}.
%C A133794 Digital clock dice integers. The number of values with 3 digits is 180. The number of values with 4 digits is 60. The number of values with 5 digits is 5400. The number of values with 6 digits is 1800. The total number of values is 7440, to the maximum 125656 equated to "12:56:56." Prime values must end with one of {11, 13, 21, 23, 31, 33, 41, 43, 51, 53}. The number of prime values with 3 digits is 23. The number of prime values with 4 digits is 6, namely 1123, 1151, 1153, 1213, 1223, 1231. Prime values with 5 digits begin 11113, 11131, 11213, 11243, 11251, 11257.
%H A133794 Nathaniel Johnston, <a href="/A133794/b133794.txt">Table of n, a(n) for n = 1..7440</a> (full sequence)
%F A133794 A057436 INTERSECTION {integers that can appear on a 12-hour digital clock, concatenated from either hours:minutes or hours:minutes:seconds}.
%e A133794 "151" equated to "1:51"; "123456" equated to "12:34:56".
%p A133794 c:=0: for h from 0 to 12 do for m from 0 to 59 do for s from 0 to 59 do t:=10000*h+100*m+s: d:=convert(t,base,10): if(t>100 and (h>0 or m<=12) and numboccur(d,0)=0 and numboccur(d,7)=0 and numboccur(d,8)=0 and numboccur(d,9)=0)then printf("%d, ", t): c:=c+1: fi: od: if(c>=80)then break: fi: od: od: # _Nathaniel Johnston_, May 17 2011
%t A133794 FromDigits/@Flatten[Table[{h,m1,m2},{h,6},{m1,5},{m2,6}],2] (* _Harvey P. Dale_, Mar 13 2023 *)
%Y A133794 Cf. A000040, A036960, A052382, A057436, A133783, index for "digital clock".
%K A133794 easy,fini,full,nonn,base,less,dumb
%O A133794 1,1
%A A133794 _Jonathan Vos Post_, Jan 05 2008
%E A133794 Comments corrected by _Nathaniel Johnston_, May 17 2011