A054215 Squares that are concatenations of two consecutive decreasing numbers.

8281, 82428241, 98029801, 538277538276, 998002998001, 7783702677837025, 9998000299980001, 79225472657922547264, 86432513458643251344, 92237976109223797609, 99998000029999800001, 106710893290106710893289

Offset

1,1

Comments

Infinitely many terms of this sequence are provided by A168624(k)^2 for k>0. - Bruno Berselli, Mar 13 2018

References

Luca, Florian, and Pantelimon Stănică. "Perfect Squares as Concatenation of Consecutive Integers." The American Mathematical Monthly 126.8 (2019): 728-734.

Links

Table of n, a(n) for n=1..12.

Formula

a(n) = concatenation of A054214(n) and A054214(n)-1. - Max Alekseyev, May 14 2007

Example

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

Crossrefs

Cf. A054214, A054216, A030465, A030466, A030467, A020339, A020340.

Sequence in context: A064014 A203881 A145527 * A031589 A031769 A280872

Adjacent sequences: A054212 A054213 A054214 * A054216 A054217 A054218

Keyword

nonn,base

Author

Patrick De Geest, Feb 15 2000

Extensions

More terms from Max Alekseyev, May 14 2007

82848241 corrected to 82428241 by Dominick Cancilla, Jul 21 2010

Status

approved