A116098
Numbers k such that k concatenated with k-9 gives the product of two numbers which differ by 6.
Original entry on oeis.org
11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001, 1000000001, 10000000001, 13223140496, 20661157025, 29752066116, 40495867769, 52892561984, 66942148761, 82644628100, 100000000001, 1000000000001
Offset: 1
100000001//99999992 = 99999998 * 100000004, where // denotes
concatenation.
-
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
A116129
Numbers k such that k concatenated with k-4 gives the product of two numbers which differ by 4.
Original entry on oeis.org
11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001, 1000000001, 10000000001, 13223140496, 20661157025, 29752066116, 40495867769, 52892561984, 66942148761, 82644628100, 100000000001, 1000000000001
Offset: 1
100000001//99999997 = 99999999 * 100000003, where // denotes concatenation.
-
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
A116122
Numbers k such that k concatenated with k-5 gives the product of two numbers which differ by 3.
Original entry on oeis.org
92185, 1453156572932210152879253333913, 3829098407015032018435618903285, 1017438814759112270449904796121753809
Offset: 1
92185//92180 = 96012 * 96015, where // denotes concatenation.
A116143
Numbers k such that k concatenated with k-2 gives the product of two numbers which differ by 3.
Original entry on oeis.org
10, 100, 132, 406, 510, 852, 1000, 7930, 10000, 66942, 100000, 113322, 440056, 1000000, 5289256, 10000000, 58477510, 100000000, 111333222, 164378892, 183673470, 200444410, 206611570, 224376732, 277008310, 297520662
Offset: 1
A116259
n times n+3 gives the concatenation of two numbers m and m-4.
Original entry on oeis.org
7282817, 8171727, 4550754022124826466, 5449245977875173532, 8176518705147900805, 8951999555715882882349355522888, 9861090464806791973258446431979
Offset: 1
8171727 * 8171730 = 6677714//6677710, where // denotes
concatenation.
Showing 1-5 of 5 results.
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