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A035519 Rare numbers: n-r and n+r are both perfect squares, where r is reverse of n and n is non-palindromic. 3
65, 621770, 281089082, 2022652202, 2042832002, 868591084757, 872546974178, 872568754178, 6979302951885, 20313693904202, 20313839704202, 20331657922202, 20331875722202, 20333875702202, 40313893704200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

There are 75 terms up to 10^19.

REFERENCES

Gupta, Shyam Sunder: Systematic computations of rare numbers, The Mathematics Education, Vol. XXXII, No. 3, Sept. 1998

LINKS

Table of n, a(n) for n=1..15.

Shyam Sunder Gupta, Rare Numbers

R. K. Guy, Conway's RATS and other reversals, Unsolved Problems Column, American Math. Monthly, page 425, May 1989.

R. K. Guy, Unsolved problems come of Age, American Math. Monthly, page 908, Dec. 1989.

EXAMPLE

65 - 56 = 9 and 65 + 56 = 121 are both squares.

MATHEMATICA

r[n_]:=FromDigits[Reverse[IntegerDigits[n, 10]], 10]; f[n_]:=n!=r[n]&&IntegerQ[Sqrt[n-r[n]]]&&IntegerQ[Sqrt[n+r[n]]]; Timing[lst={}; Do[If[f[n], AppendTo[lst, n]], {n, 11, 15!}]; lst] (* Vladimir Joseph Stephan Orlovsky, Oct 10 2009 *)

CROSSREFS

Cf. A059755.

Sequence in context: A015039 A238612 A185823 * A238842 A059755 A215657

Adjacent sequences:  A035516 A035517 A035518 * A035520 A035521 A035522

KEYWORD

nonn,base,nice

AUTHOR

Shyam Sunder Gupta, Dec 11 1999

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.