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A116129 Numbers k such that k concatenated with k-4 gives the product of two numbers which differ by 4.

%I A116129 #17 Jul 20 2021 23:43:19
%S A116129 11,101,1001,10001,100001,1000001,10000001,100000001,1000000001,
%T A116129 10000000001,13223140496,20661157025,29752066116,40495867769,
%U A116129 52892561984,66942148761,82644628100,100000000001,1000000000001
%N A116129 Numbers k such that k concatenated with k-4 gives the product of two numbers which differ by 4.
%C A116129 From _Robert Israel_, Aug 13 2018: (Start)
%C A116129 Contains, and appears to be identical to, A116098.
%C A116129 Numbers k such that (10^d+1)*k is a square, where k-4 has d digits. (End)
%e A116129 100000001//99999997 = 99999999 * 100000003, where // denotes concatenation.
%p A116129 g:= proc(d) local r,c,a,b;
%p A116129    r:= mul(t[1],t=select(s -> s[2]::odd, ifactors(10^d+1)[2]));
%p A116129    c:= ceil((10^(d-1)+4)/r);
%p A116129    a:= isqrt(c);
%p A116129    if a^2 < c then a:= a+1 fi;
%p A116129    c:= floor((10^d+3)/r);
%p A116129    b:= isqrt(c);
%p A116129    if b^2 > c then b:= b-1 fi;
%p A116129    seq(r*y^2, y = a..b)
%p A116129 end proc:
%p A116129 map(g, [$1..60]); # _Robert Israel_, Aug 13 2018
%Y A116129 Cf. A116098, A054214, A116128, A116130, A116136, A116260.
%K A116129 nonn,base
%O A116129 1,1
%A A116129 _Giovanni Resta_, Feb 06 2006