A342582 a(n) is the least multiple of n that is a "binary antipalindrome" (i.e., an element of A035928).

2, 2, 12, 12, 10, 12, 42, 56, 558, 10, 682, 12, 52, 42, 150, 240, 170, 558, 38, 240, 42, 682, 598, 240, 150, 52, 3132, 56, 232, 150, 558, 992, 8382, 170, 2730, 936, 666, 38, 936, 240, 738, 42, 3010, 3784, 535230, 598, 11938, 240, 2254, 150, 204, 52, 212, 3132

Offset: 1

Author

Rémy Sigrist, Mar 15 2021

Keywords

• nonn
• base

Comments

This sequence has similarities with A141709.

Examples

			For n = 42:
- 42 is a binary antipalindrome,
- so a(42) = 42.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A342582

Crossrefs

Cf. A035928, A141709, A318569.

Programs

PARI

See Links section.

Python

def comp(s): z, o = ord('0'), ord('1'); return s.translate({z:o, o:z})
def BCR(n): return int(comp(bin(n)[2:])[::-1], 2)
def bin_anti_pal(n): return BCR(n) == n
def a(n):
    kn = n
    while not bin_anti_pal(kn): kn += n
    return kn
print([a(n) for n in range(1, 55)]) # Michael S. Branicky, Mar 15 2021

Formula

a(n) = n * A318569(n).