A116099
Numbers k such that k concatenated with k-9 gives the product of two numbers which differ by 7.
Original entry on oeis.org
69, 59898667, 79493157, 13412927190959690154913903, 14163000698458955079906403, 38895475965785687555173929, 40165600438484442828161229, 74294440818366638194239027
Offset: 1
79493157//79493154 = 89158933 * 89158938, where // denotes concatenation.
79493157//79493158 = 89158934 * 89158937.
79493157//79493160 = 89158935 * 89158936.
79493157//79493148 = 89158932 * 89158939.
A116106
Numbers k such that k concatenated with k-8 gives the product of two numbers which differ by 6.
Original entry on oeis.org
9, 13, 99, 103, 183, 328, 528, 715, 999, 1003, 6099, 9999, 10003, 13224, 40495, 99999, 100003, 106755, 453288, 999999, 1000003, 2066115, 2975208, 9999999, 10000003, 22145328, 28027683, 99999999, 100000003, 110213248, 110667555
Offset: 1
999999999//999999991 = 999999997 * 1000000003, where // denotes concatenation.
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
A116097
Numbers k such that k concatenated with k-9 gives the product of two numbers which differ by 5.
Original entry on oeis.org
92185, 1453156572932210152879253333913, 3829098407015032018435618903285, 1017438814759112270449904796121753809
Offset: 1
92185//92176 = 96011 * 96016, where // denotes concatenation.
A116229
Numbers k such that k*(k+6) gives the concatenation of two numbers m and m-9.
Original entry on oeis.org
8, 98, 998, 9998, 99998, 999998, 9999998, 99999998, 999999998, 9999999998, 36363636361, 45454545452, 54545454543, 63636363634, 72727272725, 81818181816, 90909090907, 99999999998, 999999999998, 9999999999998
Offset: 1
99999998 * 100000004 = 100000001//99999992, where // denotes concatenation.
Showing 1-5 of 5 results.
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