login
A327143
Variation on Golomb's sequence starting with (1,2): a(n)=length of n-th run of both consecutive integers and consecutive digits with same parity.
1
1, 2, 4, 3, 5, 7, 9, 6, 8, 2111110, 2000001, 11, 13, 15, 17, 20, 22, 24, 111111110, 210, 10, 11110, 101, 19, 21, 31, 33, 23, 35, 37, 39, 26, 28, 110, 211110, 12, 14, 103, 51, 2001, 25, 53, 27, 55, 57, 11112, 212, 40, 16, 42, 1110, 21110, 44, 111110, 46, 11111110, 48, 1111111110, 21111110, 2111111110, 1112, 18, 112
OFFSET
1,2
COMMENTS
Among the first 10000 terms the largest value is a(7898)=211111111111111111111111111110 and the smallest value not occurring is 29. - Lars Blomberg, Jan 10 2020
LINKS
EXAMPLE
The sequence's start is reordered herunder in two ways: the first one to check the runs of consecutive integers, the second one to check the runs of consecutive digits.
Start = 1,2,4,3,5,7,9,6,8,2111110,2000001,11,13,15,17,...
#1 Golomb's variation (integers):
1, ---------------> size 1 block of odd integers
2,4, -------------> size 2 block of even integers
3,5,7,9, ---------> size 4 block of odd integers
6,8,2111110, -----> size 3 block of even integers
2000001,11,13,15,17, size 5 block of odd integers
...
#2 Golomb's variation (digits):
Start = 1,2,4,3,5,7,9,6,8,2111110,2000001,11,13,15,17,...
1, ----> size 1 block of odd digits
2,4, --> size 2 block of even digits
3,5,7,9, size 4 block of odd digits
6,8,2 size 3 block of even digits
11111 size 5 block of odd digits
0,200000 size 7 block of even digits
In both variations, the successive sizes rebuild the sequence.
CROSSREFS
Cf. A093506 (Variation on Golomb's sequence starting with (1,2): a(n)=length of n-th run of consecutive integers with same parity).
Sequence in context: A093506 A307485 A238980 * A343313 A082006 A277375
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Lars Blomberg, Jan 05 2020
STATUS
approved