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

1,2

Comments

A variant of A093848.

Links

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

Example

(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.

Prog

(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

Crossrefs

Cf. A093848, A101316

Sequence in context: A375927 A098794 A256228 * A169581 A184858 A083026

Adjacent sequences: A114052 A114053 A114054 * A114056 A114057 A114058

Keyword

base,easy,nonn

Author

Eric Angelini, Feb 02 2006

Extensions

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

Status

approved