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 A115531 Numbers k such that the concatenation of k with 3*k gives a square. 1
 816326530612244897959183673469388, 1836734693877551020408163265306123, 3265306122448979591836734693877552, 3746097814776274713839750260145681581685744016649323621228 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If 3+10^m is not squarefree, say 3+10^m = u^2*v where v is squarefree, then the terms with length m are t^2*v where 10^m > 3*t^2*v >= 10^(m-1).  The first m for which 3+10^m is not squarefree are 34, 59, 60, 61, 67. - Robert Israel, Aug 07 2019 Since 3+10^m is divisible by 7^2 for m = 34 + 42*k, the sequence contains 4*(3+10^m)/49, 9*(3+10^m)/49 and 16*(3+10^m)/49 for such m, and in particular is infinite. - Robert Israel, Aug 08 2019 LINKS Robert Israel, Table of n, a(n) for n = 1..113 MAPLE Res:= NULL: for m from 1 to 67 do if not numtheory:-issqrfree(3+10^m) then    F:= select(t -> t=1, ifactors(3+10^m));    v:= mul(t, t=F);    Res:= Res, seq(t^2*v, t = ceil(sqrt(10^(m-1)/(3*v))) .. floor(sqrt(10^m/(3*v)))) fi od: Res;  # Robert Israel, Aug 07 2019 CROSSREFS Cf. A102567, A106497, A115527 - A115556. Sequence in context: A338964 A277140 A083104 * A095460 A083103 A115532 Adjacent sequences:  A115528 A115529 A115530 * A115532 A115533 A115534 KEYWORD nonn,base AUTHOR Giovanni Resta, Jan 25 2006 STATUS approved

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Last modified July 3 11:18 EDT 2022. Contains 355050 sequences. (Running on oeis4.)