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Search: id:A115438
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| A115438 |
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Numbers n such that the square of n is the concatenation of two numbers k and k+4. |
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+0
12
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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 (mymontain(AT)yahoo.com), Nov 26 2006
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EXAMPLE
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120085_120089 = 346533^2.
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CROSSREFS
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Cf. A030467, A106497, A115437, A115427, A115439, A115440, A115441, A115442, A115443, A115444, A115445, A115446, A115447.
Sequence in context: A127456 A114484 A051981 this_sequence A134549 A084876 A060339
Adjacent sequences: A115435 A115436 A115437 this_sequence A115439 A115440 A115441
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KEYWORD
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base,nonn,new
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AUTHOR
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Giovanni Resta (g.resta(AT)iit.cnr.it), Jan 24 2006
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EXTENSIONS
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The initial "2" (which is admittedly somewhat dubious) added by njas, Aug 13 2008
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