cp's OEIS Frontend

A116098 Numbers k such that k concatenated with k-9 gives the product of two numbers which differ by 6.

%I A116098 #16 Jul 21 2021 22:45:51
%S A116098 11,101,1001,10001,100001,1000001,10000001,100000001,1000000001,
%T A116098 10000000001,13223140496,20661157025,29752066116,40495867769,
%U A116098 52892561984,66942148761,82644628100,100000000001,1000000000001
%N A116098 Numbers k such that k concatenated with k-9 gives the product of two numbers which differ by 6.
%C A116098 From _Robert Israel_, Aug 13 2018: (Start)
%C A116098 Contained in, and apparently identical, to A116129.
%C A116098 Numbers k such that k*(10^d+1) is a square, where k-9 has d decimal digits.
%C A116098 (End)
%H A116098 Robert Israel, <a href="/A116098/b116098.txt">Table of n, a(n) for n = 1..134</a>
%e A116098 100000001//99999992 = 99999998 * 100000004, where // denotes
%e A116098 concatenation.
%p A116098 g:= proc(d) local r,c,a,b;
%p A116098    r:= mul(t[1],t=select(s -> s[2]::odd, ifactors(10^d+1)[2]))
%p A116098    c:= ceil((10^(d-1)+9)/r);
%p A116098    a:= isqrt(c);
%p A116098    if a^2 < c then a:= a+1 fi;
%p A116098    c:= floor((10^d+8)/r);
%p A116098    b:= isqrt(c);
%p A116098    if b^2 > c then b:= b-1 fi;
%p A116098    seq(r*y^2, y = a..b)
%p A116098 end proc:
%p A116098 seq(g(d),d=1..60); # _Robert Israel_, Aug 13 2018
%Y A116098 Cf. A116097, A116099, A116106, A054214, A116128, A116129, A116130, A116136, A116229, A116260.
%K A116098 nonn,base
%O A116098 1,1
%A A116098 _Giovanni Resta_, Feb 06 2006