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Search: id:A115437
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| A115437 |
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Numbers n such that the concatenation of n with n+4 gives a square. |
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+0
12
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| 96, 205, 300, 477, 732, 1920, 3157, 52896, 120085, 427020, 8264460, 88581312, 112000885, 112917765, 143075580, 152863360, 193537077, 233788192, 266755221, 313680096, 370908477, 386568925, 440852992, 442670220
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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1. a(n).(a(n)+4) = A115438^2 where dot denotes concatenation. 2. All numbers of the form f(n) = 4(n).2.6(n-1).70.2(n).0 where n>0 are in the sequence because if k(n) = 6(n).5.3(n).4.6(n).8 then k(n)^2 = f(n).(f(n)+4). For example f(4) = 444426667022220; k(4) = 666653333466668 and k(4)^2 = 666653333466668^2 = f(4).(f(4)+4) = 444426667022220.444426667022224. 3.All numbers of the form f(n) = 1(n).2.0(n+1).8(n).5 where n>-1 are in the sequence because if k(n) = 3(n).4.6(n).5.3(n+1) then k(n)^2 = f(n).(f(n)+4). For example f(5) = 111112000000888885; k(5) = 333334666665333333 and k(5)^2 = 333334666665333333^2 = f(5). (f(5)+4) = 111112000000888885.111112000000888889. - 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. A030465, A102567, A115426, A115428, A115429, A115430, A115431, A115432, A115433, A115434, A115435, A115436, A115438.
Sequence in context: A090762 A044428 A044809 this_sequence A110231 A108609 A125511
Adjacent sequences: A115434 A115435 A115436 this_sequence A115438 A115439 A115440
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KEYWORD
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base,nonn
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AUTHOR
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Giovanni Resta (g.resta(AT)iit.cnr.it), Jan 24 2006
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