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.

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

Author

Eric Angelini, Feb 02 2006

Keywords

• base
• easy
• nonn

Comments

A variant of A093848.

Examples

			(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.
		

Links

• Dominic McCarty, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A093848, A101316

Programs

Python

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

Extensions

Name edited, a(40) and on corrected by Dominic McCarty, Mar 18 2025