OFFSET
1,1
COMMENTS
Consider a 12-hour digital clock with 4 digits, each of which comprises 7 facets (or segments or lights). The terms of the sequence list the times of day starting with the dimmest overall display, i.e., when the fewest total facets are lit up, to the brightest overall display, i.e., when the most total facets are lit up.The terms are sorted by dimness/brightness and then by smallest-to-largest number.
If the digits are labeled A, B, C, D from left to right, digit A is completely dark from 1:00 until after 9:59, and then has 2 facets lit up from 10:00 through 12:59. Digits B and D will each display numbers from 0 to 9 and thus will have between 2 and 7 facets lit up. Digit C will display numbers from 0 to 5 and thus will have between 2 and 6 facets lit up.
The sequence displays each time of day without the customary colon separating hours from minutes, so for example 12:36 is displayed as 1236 and 9:14 is displayed as 914.
The dimmest display is for 1:11 (or 111) when 6 facets in total are lit up. The brightest display is for 10:08 (or 1008) when 21 facets are lit up. The sequence has 720 terms altogether.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..720
EXAMPLE
111 is displayed with digit A dark and with 2 facets of each of digits B, C, and D lit up. Thus 111 has a total of 6 facets lit up. 1008 is displayed with 2 facets of digit A lit up, with 6 facets of digits B and C lit up, and with 7 facets of digit D lit up. Thus 1008 has a total of 21 facets lit up.
MATHEMATICA
SortBy[{#, Total[IntegerDigits[#]/.{0->6, 1->2, 2->5, 3->5, 7->3, 8->7, 9->6}]}&/@ FromDigits/@Flatten[Table[Join[IntegerDigits[ h], PadLeft[ IntegerDigits[ m], 2, 0]], {h, 12}, {m, 0, 59}], 1], {Last, First}][[All, 1]]
CROSSREFS
KEYWORD
nonn,fini,full,base
AUTHOR
Harvey P. Dale, Oct 10 2020.
STATUS
approved