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A116129 Numbers k such that k concatenated with k-4 gives the product of two numbers which differ by 4. 5
11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001, 1000000001, 10000000001, 13223140496, 20661157025, 29752066116, 40495867769, 52892561984, 66942148761, 82644628100, 100000000001, 1000000000001 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A118937 A031997 A116098 * A056810 A000533 A147759
KEYWORD
nonn,base
AUTHOR
Giovanni Resta, Feb 06 2006
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)