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

1,2

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Intersection of A006995 and A049445.

Cf. A082232.

Sequence in context: A032535 A022745 A225967 * A004324 A243421 A028053

Adjacent sequences: A334526 A334527 A334528 * A334530 A334531 A334532

Keyword

nonn,base

Author

Amiram Eldar, May 05 2020

Status

approved