Original entry on oeis.org
3, 6, 8, 10, 13, 15, 17, 19, 22, 24, 26, 28, 30, 32, 35, 37, 39, 41, 43, 45, 47, 49, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 123
Offset: 1
A169864
The sequence S of a pair S, T generalizing Golomb's sequence A001462 and the pair A093848, A169863. See Comments for definition.
Original entry on oeis.org
1, 3, 4, 6, 8, 10, 12, 13, 15, 17, 19, 21, 23, 25, 26, 28, 30, 32, 34, 36, 38, 40, 42, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 91, 93
Offset: 1
N. J. A. Sloane, Jun 27 2010, following a posting from Eric Angelini to the Sequence Fans Mailing List, Jun 22, 2010
A169865
The sequence T of a pair S, T generalizing Golomb's sequence A001462 and the pair A093848, A169863. See Comments for definition.
Original entry on oeis.org
2, 5, 7, 9, 11, 14, 16, 18, 20, 22, 24, 27, 29, 31, 33, 35, 37, 39, 41, 44, 46
Offset: 1
N. J. A. Sloane, Jun 27 2010, following a posting from Eric Angelini to the Sequence Fans Mailing List, Jun 22, 2010
A169866
The sequence S of a pair of complementary sequences (S, T) which are similar to the pairs (A093848, A169863), (A169864, A169865), except that here the lengths of the equal-parity runs of one sequence are given by the other.
Original entry on oeis.org
1, 3, 4, 6, 8, 10, 12, 11, 13, 15, 17, 19, 21, 23, 22, 24, 26, 28, 30, 32, 34, 36, 38, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86
Offset: 1
N. J. A. Sloane, Jun 27 2010, following a posting from Eric Angelini to the Sequence Fans Mailing List, Jun 22, 2010
A169867
The sequence T of a pair of complementary sequences (S, T) which are similar to the pairs (A093848, A169863), (A169864, A169865), except that here the lengths of the equal-parity runs of one sequence are given by the other.
Original entry on oeis.org
2, 5, 7, 9, 14, 16, 18, 20, 25, 27, 29, 31, 33, 35, 40, 42, 44, 46, 48, 50, 52, 54, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110
Offset: 1
N. J. A. Sloane, Jun 27 2010, following a posting from Eric Angelini to the Sequence Fans Mailing List, Jun 22, 2010
A114055
Lexicographically earliest strictly increasing sequence such that the run lengths of digits with equal parity in the sequence's digit stream yield the sequence itself.
Original entry on oeis.org
1, 2, 4, 5, 7, 9, 10, 20, 22, 31, 33, 35, 36, 40, 42, 44, 46, 51, 53, 55, 57, 59, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88, 91, 93, 95, 97, 99, 111, 113, 115, 117, 200, 202, 204, 206, 208, 220, 222, 224, 226, 228, 231, 311, 313, 315, 317, 319, 331, 333, 335, 337
Offset: 1
(1),(2,4),(5,7,9,1)(0,20,22),(31,33,35,3)(6,40,42,44,46),(51,53,55,57,59),(60,62,64,66,68,80,82,84,86,88)... Those runs of equal parity digits are of length 1,2,4,5,7,9,10,20... which is the sequence itself.
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from itertools import groupby
from itertools import count
a = [1,2]
while len(a)<100:a.append(next(k for k in count(a[-1]+1)if (b := [len(list(g))for _,g in(groupby(list(map(lambda d:int(d)%2,"".join(map(str,a))+str(k)))))])and all(b[i]==a[i]for i in range(len(b)-1))and not b[-1]>a[len(b)-1]))
print(a) # Dominic McCarty, Mar 18 2025
Showing 1-6 of 6 results.
Comments