A241096 Palindromes in base 16 whose squares are also palindromes.

1, 2, 3, 11, 22, 101, 111, 121, 131, 202, 212, 222, 1001, 1111, 1221, 2002, 2112, 10001, 10101, 10201, 10301, 11011, 11111, 11211, 11311, 12021, 12121, 12221, 20002, 20102, 20202, 21012, 21112, 21212, 100001, 101101, 102201, 110011, 111111, 112211, 120021

Offset: 1

Author

J. Lowell, Apr 26 2014

Keywords

• nonn
• base

Examples

			131 is a term of this sequence because (unlike in base 10, where squaring 131 carries a 1 into the thousands place so that 131^2 is the non-palindromic number 17161) in base 16, 131^2 is 16B61.
141 is not a term because, even in base 16, a 1 is carried into the next place, so the result (19281) is not palindromic.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A057135.

Programs

Sage

L=[]
for x in [1..100000]:
    M=x.digits(base=16)
    N=M[::-1]
    if N == M:
        d=x^2
        D=d.digits(base=16)
        E=D[::-1]
        if D == E:
            MM=(str(x) for x in M)
            L.append(Integer(''.join(MM)))
L # Tom Edgar, Apr 29 2014

Extensions

a(35)-a(41) from Lars Blomberg, Oct 23 2014