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

1,2

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A057135.

Sequence in context: A118595 A229549 A229804 * A057135 A229805 A104075

Adjacent sequences: A241093 A241094 A241095 * A241097 A241098 A241099

Keyword

nonn,base

Author

J. Lowell, Apr 26 2014

Extensions

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

Status

approved