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

111, 112, 113, 114, 115, 116, 121, 122, 123, 124, 125, 126, 131, 132, 133, 134, 135, 136, 141, 142, 143, 144, 145, 146, 151, 152, 153, 154, 155, 156, 211, 212, 213, 214, 215, 216, 221, 222, 223, 224, 225, 226, 231, 232, 233, 234, 235, 236, 241, 242, 243

Offset: 1

Author

Jonathan Vos Post, Jan 05 2008

Keywords

• easy
• fini
• full
• nonn
• base
• less
• dumb

Comments

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.

Examples

			"151" equated to "1:51"; "123456" equated to "12:34:56".
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..7440 (full sequence)

Crossrefs

Cf. A000040, A036960, A052382, A057436, A133783, index for "digital clock".

Programs

Maple

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

Mathematica

FromDigits/@Flatten[Table[{h,m1,m2},{h,6},{m1,5},{m2,6}],2] (* Harvey P. Dale, Mar 13 2023 *)

Formula

A057436 INTERSECTION {integers that can appear on a 12-hour digital clock, concatenated from either hours:minutes or hours:minutes:seconds}.

Extensions

Comments corrected by Nathaniel Johnston, May 17 2011