A256515 Nonpalindromic positive integers k such that the absolute value of k^2 - reverse(k)^2 is a square.

56, 65, 5265, 5625, 5656, 6565, 12705, 44370, 50721, 51557, 55517, 56056, 59248, 65065, 71555, 75515, 84295, 139755, 273728, 360145, 481610, 523908, 541063, 557931, 560056, 560439, 565656, 606056, 621770, 650065, 650606, 656565, 697996, 699796, 809325, 827372

Offset: 1

Author

Bui Quang Tuan, Apr 01 2015

Keywords

• nonn
• base

Examples

			The nonpalindromic number 5265 is a term because abs(5265^2 - 5625^2) = 1980^2.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..425 (all terms < 10^11; terms 1..68 from Bui Quang Tuan)

Crossrefs

Cf. A004086 (digit reversal), A202386, A068536.

Programs

Magma

[n: n in [0..10^6] | Intseq(n) ne Reverse(Intseq(n)) and IsSquare(s) where s is Abs(n^2-Seqint(Reverse(Intseq(n)))^2)]; // Bruno Berselli, Apr 01 2015

Mathematica

Select[Range[200000], ! PalindromeQ@ # && IntegerQ@ Sqrt@ Abs[#^2 - IntegerReverse[#]^2] &] (* Michael De Vlieger, Mar 02 2022 *)

Python

from sympy.ntheory.primetest import is_square
def R(n): return int(str(n)[::-1])
def ok(n): Rn = R(n); return n != Rn and is_square(abs(n**2 - Rn**2))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Mar 02 2022