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, 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

Lars Blomberg, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A327140 A327141 A327142 * A327144 A327145 A327146

Keyword

base,nonn

Author

Eric Angelini and Lars Blomberg, Jan 05 2020

Status

approved