Original entry on oeis.org
0, 10, 20, 100, 30, 102, 40, 101, 203, 105, 60, 1024, 300, 107, 200, 150, 304, 1026, 80, 109, 230, 10457, 0, 120, 306, 110, 204, 1058, 303, 10279, 0, 1046, 302, 501, 0, 201, 3048, 170, 206, 1059, 330, 1042, 0, 1000, 320, 105678, 400, 210, 3000, 190, 202, 1045, 360, 1027, 800, 1001, 2034, 510, 0, 10269
Offset: 1
The finite sequence A375232 ends with 80, 109, 230, 10457. If we extend it with a(23) = 0, we can compute a(24) = 120, a(25) = 306 then 110, 204, 1058, 303 and 10279. No more integers are available at that stage. But, again, we can extend the sequence with a(31) = 0, then a(32) = 1046 and 302, 501, 0, 201, 3048, 170, etc.
A repeated single 0 is counted as a term of the sequence.
A376150
Define b_n(k) to be the lexicographically earliest sequence of distinct nonnegative integers with the property that two terms that contain the digit "d" are always separated by exactly "d" terms that do not contain the digit "d", in base n. a(n) is the number of terms in b_n(k).
Original entry on oeis.org
2, 4, 6, 10, 10, 18, 18, 22, 22, 30, 30, 34, 42, 42, 78, 78, 78, 78, 102, 102, 114, 114, 114, 114, 142, 142, 142, 142, 214, 214, 214, 214, 214, 214, 214, 222, 274, 274, 274, 274, 274, 354, 354, 354, 354, 354, 354, 642, 642, 642, 642, 642, 642, 642, 642
Offset: 2
For n = 5:
b_5(1) = 0; as this contains the digit 0, b_5(2), b_5(3) etc. must also contain a 0
b_5(2) = 10 (= 5 in decimal); must contain a 0 from b_5(1); as this contains the digit 1, b_5(4), b_5(6) etc. must also contain a 1, and all other terms must not contain a 1
b_5(3) = 20; must have 0 but not 1
b_5(4) = 100; must have 0 and 1 but not 2
b_5(5) = 30; must have 0 but not 1 or 2
b_5(6) = 102; must have 0, 1, and 2, but not 3
b_5(7) = 40; must have 0 but not 1, 2, or 3
b_5(8) = 101; must have 0 and 1 but not 2, 3, or 4
b_5(9) = 203; must have 0, 2, and 3, but not 1 or 4
b_5(10) = 110; must have 0 and 1 but not 2, 3, or 4
b_5(11) = ---; must have 0 but not 1, 2, 3, or 4 - the only number that fills this condition is 0, but 0 already appears in the sequence, so the sequence terminates after ten terms, and a(5) = 10
Showing 1-2 of 2 results.
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