A365374 Numbers k such that squaring each digit and concatenating them forms a palindrome.

0, 1, 2, 3, 11, 19, 22, 28, 33, 37, 41, 72, 101, 111, 121, 131, 199, 202, 212, 222, 232, 288, 303, 313, 323, 327, 333, 377, 441, 461, 732, 772, 1001, 1111, 1191, 1221, 1281, 1331, 1371, 1411, 1721, 1919, 1999, 2002, 2112, 2192, 2222, 2282, 2332, 2372, 2412, 2722, 2828, 2888

Offset

1,3

Comments

The sequence is infinite since if k is a term then so is 1k1.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

k(6) = 19 becomes 181 as 1^2 = 1 and 9^2 = 81;
k(7) = 22 becomes  44 as 2^2 = 4 and 2^2 =  4;
k(8) = 28 becomes 464 as 2^2 = 4 and 8^2 = 64; etc.

Mathematica

Select[Range[0, 3000], PalindromeQ@FromDigits@Flatten[IntegerDigits/@(IntegerDigits@#^2)]&]

Prog

(Python)
def ok(n): return (s:="".join(str(int(d)**2) for d in str(n))) == s[::-1]
print([k for k in range(3000) if ok(k)]) # Michael S. Branicky, Oct 05 2023

Crossrefs

Cf. A258373, A366198.

Sequence in context: A025101 A025105 A257979 * A095984 A229550 A172258

Adjacent sequences: A365371 A365372 A365373 * A365375 A365376 A365377

Keyword

base,nonn

Author

Eric Angelini and Giorgos Kalogeropoulos, Oct 05 2023

Status

approved