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Revision History for A329818 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Look left and tell the least frequent digit string; a(0) = 0, a(n) = concat(c,s), where c > 0 is the number of times the string s, composed of one or more digits, has appeared in a(0) to a(n-1) such that a(n) is minimal. Digit strings with leading zeros are ignored.
(history; published version)
#24 by N. J. A. Sloane at Sun Nov 24 01:59:59 EST 2019
STATUS

proposed

approved

#23 by Scott R. Shannon at Sat Nov 23 21:45:33 EST 2019
STATUS

editing

proposed

#22 by Scott R. Shannon at Sat Nov 23 21:42:58 EST 2019
COMMENTS

This sequence is the same as A329447 up to a(5655) = 100. After that, as a(2) = 11 and '11' has only appeared once, the next smallest value is that of 'one 11', that is 111.

LINKS

Scott R. Shannon, <a href="/A329818/b329818.txt">Table of n, a(n) for n = 0..20000</a>

STATUS

approved

editing

Discussion
Sat Nov 23
21:45
Scott R. Shannon: Added bfile. Also fixed error in comment... a(55) = 100.
#21 by N. J. A. Sloane at Sat Nov 23 21:16:17 EST 2019
STATUS

proposed

approved

#20 by Scott R. Shannon at Fri Nov 22 19:39:28 EST 2019
STATUS

editing

proposed

#19 by Scott R. Shannon at Fri Nov 22 19:38:07 EST 2019
NAME

Look left and tell the least frequent digit string; a(0) = 0, a(n) = concat(c,s), where c > 0 is the number of times the string s, composed of one or more digits, has appeared so far in a(0) to a(n-1) such that a(n) is minimal. Digit strings with leading zeros are ignored.

COMMENTS

This is a variation on A329447. Instead of just considering the number of times the digits 0 to 9 have appeared so far in the sequence, we consider all numbers formed by the substrings of each previous entry; from single digits to the entire entry itself. Each value of a(n) is determined by considering the count of all the substrings occurring so far in a(0) to a(n-1) and then choosing the one which forms the lowest number when the count of that substring is concatenated with the substring itself.

Discussion
Fri Nov 22
19:39
Scott R. Shannon: made some changes to hopefully clarify the above
#18 by Scott R. Shannon at Fri Nov 22 18:06:48 EST 2019
NAME

Look left and tell the least frequent digit string; a(0) = 0, a(n) = concat(c + ,s, ), where c > 0 is the number of times the string s, composed of one or more digits, has appeared so far such that the number c concatenated with s a(n) is minimal. Digit strings with leading zeros are ignored.

STATUS

proposed

editing

#17 by Scott R. Shannon at Fri Nov 22 01:18:23 EST 2019
STATUS

editing

proposed

Discussion
Fri Nov 22
12:31
M. F. Hasler: Do you really mean c+s or rather concat(c,s) ?
12:34
M. F. Hasler: Actually you would not need to impose "strings with leanding 0's are ignored" because the string s itself doesn't appear in the sequence, only prefixed with c, so one could well allow stings with leading zeros. (I don't mean to change that here but it could be a separate variant of these seq's)
12:37
M. F. Hasler: Also maybe please clarify whether "so far" means only preceding terms or does it include a(n) itself? (there is "previous entries" then "the entire entry itself", the former seems to mean "terms" but the latter maybe "the entire sequence" ?)
#16 by Scott R. Shannon at Fri Nov 22 00:43:30 EST 2019
NAME

Look left and tell the least frequent digit string; a(0) = 0, a(n) = a c + b, s, where a c > 0 is the number of times the string b, s, composed of one or more digits, has appeared so far such that the number a c concatenated with b s is minimal. Digit strings with leading zeros are ignored.

STATUS

proposed

editing

Discussion
Fri Nov 22
00:44
Scott R. Shannon: thanks yes I guess the 'a' with a(n) wasnt the best. changed to c and s for count and string. hope thats ok
#15 by Scott R. Shannon at Thu Nov 21 23:34:58 EST 2019
STATUS

editing

proposed

Discussion
Fri Nov 22
00:21
Rémy Sigrist: maybe u + v instead of a + b