A115438 Numbers whose square is the concatenation of two numbers k and k+4.

2, 310, 453, 548, 691, 856, 4382, 5619, 72730, 346533, 653468, 9090908, 94117646, 334665333, 336032387, 378253328, 390977442, 439928491, 483516486, 516483515, 560071510, 609022559, 621746673, 663967614, 665334668

Offset

1,1

Comments

From Farideh Firoozbakht, Nov 26 2006: (Start)

1. All numbers of the form f(n)=3(n).4.6(n).5.3(n+1) are in the sequence because if k(n)=1(n).2.0(n+1).8(n).5 then f(n)^2= k(n).(k(n)+4). For example f(3)=333466653333; k(3)=111200008885 and f(3)^2=333466653333^2=k(3).(k(3)+4)=111200008885.111200008889.

2. All numbers of the form g(n)=6(n).5.3(n).4.6(n).8 are in the sequence because g(0)=548 is in the sequence(548^2=300.304) and for n>0 if h(n)=4(n).2.6(n-1).70.2(n).0 then g(n)^2=h(n).(h(n)+4). For example g(5)=666665333334666668; h(5)=444442666670222220 and g(5)^2=h(5).(h(5)+4)=444442666670222220.444442666670222224. (End)

Links

Table of n, a(n) for n=1..25.

Example

120085_120089 = 346533^2.

Crossrefs

Cf. A030467, A106497, A115437, A115427, A115439, A115440, A115441, A115442, A115443, A115444, A115445, A115446, A115447.

Sequence in context: A359208 A199946 A142800 * A106718 A119779 A118579

Adjacent sequences: A115435 A115436 A115437 * A115439 A115440 A115441

Keyword

base,nonn

Author

Giovanni Resta, Jan 24 2006

Extensions

The initial "2" (which is admittedly somewhat dubious) added by N. J. A. Sloane, Aug 13 2008

Status

approved