A202386 Nonpalindromic numbers m such that the difference between the square of m and the square of the reversal of m is itself a perfect square. Numbers ending in 0 are excluded.

65, 5625, 6565, 50721, 65065, 71555, 75515, 84295, 541063, 557931, 650065, 650606, 656565, 699796, 809325, 827372, 934065, 2855182, 4637061, 4854634, 5791775, 5883141, 5951693, 6129084, 6500065, 6731076, 6752626, 6791774, 7768827, 8084505, 9349065

Offset: 1

Author

Arkadiusz Wesolowski, Dec 18 2011

Keywords

• nonn
• base

Comments

This sequence is infinite because 65*10^k + 65 is a term for all k > 1.

Examples

			5625 belongs to this sequence because 5625^2 - 5265^2 = 1980^2.
		

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1996, p. 147.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..200
• Sheng Jiang and Rui-Chen Chen, Digits reversed Pythagorean triples, International Journal of Mathematical Education in Science and Technology, volume 29, number 5, 1998, pages 689-696, see type acca-DRPT.

Crossrefs

Cf. A000290 (squares), A004086 (digit reversal).

Cf. A256515 (with abs), A068536 (with addition).

Programs

Mathematica

lst = {}; Do[a = n^2; b = FromDigits[Reverse[IntegerDigits[n]]]^2; If[MatchQ[Sqrt[a - b], _Integer] && ! a == b, AppendTo[lst, n]], {n, 85000}]; Select[lst, ! Mod[#, 10] == 0 &]

PARI

isok(m) = my(r=fromdigits(Vecrev(digits(m)))); (r != m) && (m % 10) && issquare(m^2 - r^2); \\ Michel Marcus, Feb 27 2020

Extensions

Name clarified by Michel Marcus, Feb 27 2020