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A115438 Numbers n such that the square of n is the concatenation of two numbers k and k+4. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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. - Farideh Firoozbakht, Nov 26 2006

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: A273198 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

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Last modified June 14 20:21 EDT 2021. Contains 345038 sequences. (Running on oeis4.)