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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 7 19:35 EST 2023. Contains 360128 sequences. (Running on oeis4.)