A115439 Numbers m such that the square of m is the concatenation of two numbers k and k+5.

4, 7, 45, 56, 38163, 61838, 83618, 346980, 653021, 950051, 8647555, 9534265, 8167822283, 9007920992, 9209900792, 9950000501, 4737445289221, 4990568257187, 5009431742814, 5262554710780, 8373808925585, 8626931893551, 34323166122692, 34532758615690, 49625657225895, 49835249718893

Offset

1,1

Comments

All numbers of the form f(n)=9(n).5.0(2n).5.0(n-1).1 where n>0 are in the sequence because if k(n)=9(n).0(n).25.0(n-1).9(n).6 then f(n)^2=k(n).(k(n)+5). For example f(2)=9950000501; k(2)=9900250996 and f(2)^2=9950000501^2=9900250996.9900251001 =k(2).(k(2)+5). - Farideh Firoozbakht, Nov 26 2006

m^2 = (k)|(k+5) = (k)|(k) + 5 = (10^q + 1)*k + 5 where | denotes concatenation and q is the number of digits of k gives a nonlinear equation that can be solved using the solver below. - David A. Corneth, Jan 02 2021

Links

David A. Corneth, Table of n, a(n) for n = 1..3733

Dario A. Alpern, Generic two integer variable equation solver

Example

38163^2 = 14564_14569.

Crossrefs

Cf. A030467, A057934, A106497, A115428, A115427, A115438, A115440, A115441, A115442, A115443, A115444, A115445, A115446, A115447.

Sequence in context: A199404 A284971 A139030 * A348625 A192168 A094609

Adjacent sequences: A115436 A115437 A115438 * A115440 A115441 A115442

Keyword

base,nonn

Author

Giovanni Resta, Jan 24 2006

Extensions

More terms from David A. Corneth, Jan 02 2021

Status

approved