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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. +0
3
65, 621770, 281089082, 2022652202, 2042832002, 868591084757, 872546974178, 872568754178, 6979302951885, 20313693904202, 20313839704202, 20331657922202, 20331875722202, 20333875702202, 40313893704200 (list; graph; listen)
OFFSET

1,1

REFERENCES

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

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.

LINKS

Shyam Sunder Gupta, Rare Numbers

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] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 10 2009]

CROSSREFS

Cf. A059755.

Sequence in context: A061688 A015072 A015039 this_sequence A059755 A157631 A138843

Adjacent sequences: A035516 A035517 A035518 this_sequence A035520 A035521 A035522

KEYWORD

nonn,base,nice

AUTHOR

Shyam Sunder Gupta (guptass(AT)rediffmail.com)

EXTENSIONS

There are 75 terms up to 10^19.

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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