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%I #7 Aug 26 2023 03:15:24
%S 26,66,3416102887775247376839416334668635,
%T 3756559953325598880263233435801764,4313503800489302411917772257282208
%N n times n+9 gives the concatenation of two numbers m and m+1.
%H Robert Israel, <a href="/A116300/b116300.txt">Table of n, a(n) for n = 1..28</a>
%e 66 * 75 = 49//50, where // denotes concatenation.
%p F:= proc(d) local t, g, Cands:
%p t:= 10^d+1;
%p if NumberTheory:-QuadraticResidue(85,t) <> 1 then return NULL fi;
%p Cands:= map(s -> rhs(op(s)), [msolve(x^2 + 9*x - 1, t)]);
%p g:= proc(r) local v; v:= r^2 + 9*r - 1; v >= t*(t-11)/10 and v < t*(t-2) end proc;
%p op(sort(select(g, Cands)));
%p end proc:
%p map
%p map(F, [$1..82]); # _Robert Israel_, Aug 25 2023
%Y Cf. A116169, A116293, A116299, A116306.
%K nonn,base
%O 1,1
%A _Giovanni Resta_, Feb 06 2006
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