A334529 Numbers that are both binary palindromes and binary Niven numbers.

1, 21, 273, 4161, 22517, 28347, 65793, 69905, 81913, 87381, 106483, 109483, 121143, 292721, 299593, 317273, 319449, 350933, 354101, 368589, 378653, 421811, 470951, 479831, 1049601, 1135953, 1171313, 1172721, 1208009, 1257113, 1269593, 1295481, 1332549, 1371877

Offset: 1

Author

Amiram Eldar, May 05 2020

Keywords

• nonn
• base

Examples

			21 is a term since its binary representation, 10101, is palindromic, and 1 + 0 + 1 + 0 + 1 = 3 is a divisor of 21.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A006995 and A049445.

Cf. A082232.

Programs

Mathematica

Select[Range[10^6], PalindromeQ[(d = IntegerDigits[#, 2])] && Divisible[#, Plus @@ d] &]

Python

def ok(n): b = bin(n)[2:]; return b==b[::-1] and n%sum(map(int, b)) == 0
def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
print(aupto(1371877)) # Michael S. Branicky, Jan 21 2021