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A054214 Numbers n such that n concatenated with n-1 is a square. 9
82, 8242, 9802, 538277, 998002, 77837026, 99980002, 7922547265, 8643251345, 9223797610, 9999800002, 106710893290, 453378226757, 491023832065, 945958034530, 999998000002, 11916002265170, 15790977390245, 24917378001937 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every term contains even number of digits. - Max Alekseyev, May 14 2007

If n=(10^m-1)^2+1 where m is a positive integer then n is in the sequence. Because n has 2m digits and n concatenated with n-1 is n*10^(2m)+(n-1)=(10^(2m)-10^m+1)^2. Take m=1 we get 82 the first such term. - Farideh Firoozbakht, Aug 22 2013

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

E.g. '8242' + '8242-1' gives 82428241 which is 9079^2.

CROSSREFS

Cf. A054215, A054216, A030465, A030466, A030467, A020339, A020340.

Sequence in context: A097841 A116123 A116142 * A093241 A280361 A280671

Adjacent sequences:  A054211 A054212 A054213 * A054215 A054216 A054217

KEYWORD

nonn,base

AUTHOR

Patrick De Geest, Feb 15 2000.

EXTENSIONS

More terms from Max Alekseyev, May 14 2007

STATUS

approved

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Last modified April 25 00:32 EDT 2017. Contains 285346 sequences.