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A102567
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Numbers n such that n concatenated with itself is a biperiod square.
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50
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13223140496, 20661157025, 29752066116, 40495867769, 52892561984, 66942148761, 82644628100, 183673469387755102041, 326530612244897959184, 510204081632653061225, 734693877551020408164
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OFFSET
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1,1
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COMMENTS
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Also, numbers N associated with A106497.
Also, numbers n such that n concatenated with n-1 gives the product of two numbers which differ by 2. E.g. 13223140496//13223140495 = 36363636363 * 36363636365, where // denotes concatenation. - Giovanni Resta and Franklin T. Adams-Watters, Nov 13 2006
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REFERENCES
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R. Ondrejka, Problem 1130: Biperiod Squares, Journal of Recreational Mathematics, Vol. 14:4 (1981-82), 299. Solution by F. H. Kierstead, Jr., JRM, Vol. 15:4 (1982-83), 311-312.
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LINKS
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David W. Wilson, Table of n, a(n) for n = 1..1098
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EXAMPLE
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13223140496 concatenated with 13223140496 is 1322314049613223140496 = 36363636364^2
40495867769 is in the sequence because writing it twice gives the square number 4049586776940495867769 = 63636363637^2.
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MAPLE
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with(numtheory): Digits:=50:for d from 1 to 35 do tendp1:=10^d+1: tendp1fact:=ifactors(tendp1)[2]: n:=mul(piecewise(tendp1fact[i][2] mod 2=1, tendp1fact[i][1], 1), i=1..nops(tendp1fact)):for i from ceil(sqrt((10^(d-1))/n)) to floor(sqrt((10^d-1)/n)) do printf("%d, ", n*i^2) od: od:
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CROSSREFS
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Cf. A092118, A116142, A116163, A116136, A116279.
Sequence in context: A204096 A113639 A059122 * A016932 A016992 A017160
Adjacent sequences: A102564 A102565 A102566 * A102568 A102569 A102570
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KEYWORD
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easy,nonn,base
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AUTHOR
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C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 15 2005
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EXTENSIONS
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Entry revised by N. J. A. Sloane, Nov 14 2006 and also Nov 27 2006
Definition edited and reference added by William Rex Marshall, Nov 12 2010
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STATUS
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approved
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