A029983 Squares which are palindromes in base 2.

0, 1, 9, 20457529, 143784081, 331130809, 20074072489, 1193532215121, 10036851273801, 41413201925481, 155991531977649, 320642706437001, 4665141483989281, 87463589042698969, 152191954834044129

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..22
• Patrick De Geest, Palindromic Squares in bases 2 to 17
• G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Crossrefs

Cf. A003166.

Programs

Python

from itertools import count, islice
def A029983_gen(): # generator of terms
    return filter(lambda k: (s:=bin(k)[2:])[:(t:=(len(s)+1)//2)]==s[:-t-1:-1],(k**2 for k in count(0)))
A029983_list = list(islice(A029983_gen(),10)) # Chai Wah Wu, Jun 23 2022