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

1,1

Comments

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

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.

Example

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

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 &]

Prog

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

Crossrefs

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

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

Sequence in context: A110900 A084272 A146756 * A294955 A115432 A116104

Adjacent sequences: A202383 A202384 A202385 * A202387 A202388 A202389

Keyword

nonn,base

Author

Arkadiusz Wesolowski, Dec 18 2011

Extensions

Name clarified by Michel Marcus, Feb 27 2020

Status

approved