A248171 Partition of the positive integers on minimal blocks such that concatenation of numbers in each block is an evil number (A001969). Sequence lists the evil numbers obtained in this way.

12, 3, 45, 6, 78, 9, 10, 1112, 1314, 15, 161718, 1920, 2122, 23, 24, 2526, 27, 2829, 30, 3132, 33, 34, 3536, 37383940, 414243, 4445464748, 495051, 52535455, 5657, 58, 5960, 6162, 63, 646566, 6768, 6970, 71, 72, 7374, 75, 7677787980, 818283, 8485868788, 89, 90

Offset: 1

Author

Vladimir Shevelev, Oct 03 2014

Keywords

• nonn
• base

Comments

The numbers of the consecutive positive integers over blocks of the partition are 2,1,2,1,2,1,1,2,2,1,3,2,2,1,1,2,1,...

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000069 (odious), A001969 (evil), A248009, A248138, A248140, A248172 (similar, with odious).

Programs

Python

from itertools import count
def evil(n): return bin(n)[2:].count('1') % 2 == 0
def aupton(terms):
    alst, t = [], 0
    for k in count(1):
        t = int(str(t) + str(k))
        if evil(t):
            alst.append(t)
            t = 0
            if len(alst) >= terms: return alst
print(aupton(45)) # Michael S. Branicky, Dec 03 2021

Extensions

More terms from Peter J. C. Moses, Oct 04 2014