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

11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001, 1000000001, 10000000001, 13223140496, 20661157025, 29752066116, 40495867769, 52892561984, 66942148761, 82644628100, 100000000001, 1000000000001

Offset

1,1

Comments

From Robert Israel, Aug 13 2018: (Start)

Contained in, and apparently identical, to A116129.

Numbers k such that k*(10^d+1) is a square, where k-9 has d decimal digits.

(End)

Links

Robert Israel, Table of n, a(n) for n = 1..134

Example

100000001//99999992 = 99999998 * 100000004, where // denotes
concatenation.

Maple

g:= proc(d) local r, c, a, b;
   r:= mul(t[1], t=select(s -> s[2]::odd, ifactors(10^d+1)[2]))
   c:= ceil((10^(d-1)+9)/r);
   a:= isqrt(c);
   if a^2 < c then a:= a+1 fi;
   c:= floor((10^d+8)/r);
   b:= isqrt(c);
   if b^2 > c then b:= b-1 fi;
   seq(r*y^2, y = a..b)
end proc:
seq(g(d), d=1..60); # Robert Israel, Aug 13 2018

Crossrefs

Cf. A116097, A116099, A116106, A054214, A116128, A116129, A116130, A116136, A116229, A116260.

Sequence in context: A191420 A118937 A031997 * A116129 A056810 A000533

Adjacent sequences: A116095 A116096 A116097 * A116099 A116100 A116101

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Status

approved