A116129 - OEIS

A116129

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

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

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OFFSET

1,1

COMMENTS

From Robert Israel, Aug 13 2018: (Start)

Contains, and appears to be identical to, A116098.

Numbers k such that (10^d+1)*k is a square, where k-4 has d digits. (End)

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

100000001//99999997 = 99999999 * 100000003, 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)+4)/r);

a:= isqrt(c);

if a^2 < c then a:= a+1 fi;

c:= floor((10^d+3)/r);

b:= isqrt(c);

if b^2 > c then b:= b-1 fi;

seq(r*y^2, y = a..b)

end proc:

map(g, [$1..60]); # Robert Israel, Aug 13 2018

CROSSREFS

Cf. A116098, A054214, A116128, A116130, A116136, A116260.

Sequence in context: A118937 A031997 A116098 * A056810 A000533 A147759

Adjacent sequences: A116126 A116127 A116128 * A116130 A116131 A116132

KEYWORD

nonn,base

AUTHOR

Giovanni Resta, Feb 06 2006

STATUS

approved