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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
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
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
KEYWORD
nonn,base
AUTHOR
Giovanni Resta, Jan 25 2006
STATUS
approved