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A115529 Numbers k such that the concatenation of 2*k with k gives a square. 1
1632653061224489796, 3673469387755102041, 6530612244897959184, 108166576527852893455922120064900, 130881557598702001081665765278529, 155759870200108166576527852893456, 182801514332071389940508382909681 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers of the form k = a*b^2 where 10^(d-1) <= k < 10^d and (2*10^d+1)/a is a square. - Robert Israel, Jan 13 2021

LINKS

Robert Israel, Table of n, a(n) for n = 1..36

EXAMPLE

3265306122448979592_1632653061224489796 = 5714285714285714286^2.

MAPLE

f:= proc(d) local R, q, F, G, s, t, a, u, i;

   q:= 2*10^d+1;

   F:= ifactors(q)[2];

   G:= map(t -> [t[1], floor(t[2]/2)], F);

   s:= mul(t[1]^t[2], t=G);

   R:= NULL:

   for a in numtheory:-divisors(s) do

     u:= q/a^2;

     R:= R, seq(i^2*u, i=ceil(sqrt(10^(d-1)/u))..floor(sqrt((10^d-1)/u)))

   od;

   R

end proc:

seq(f(d), d=1..33); # Robert Israel, Jan 13 2021

CROSSREFS

Cf. A102567, A106497, A115527 - A115556.

Sequence in context: A281507 A160045 A113741 * A229864 A113740 A281508

Adjacent sequences:  A115526 A115527 A115528 * A115530 A115531 A115532

KEYWORD

nonn,base

AUTHOR

Giovanni Resta, Jan 25 2006

STATUS

approved

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)