A116291
Numbers k such that k * (k + 7) is the concatenation of a number m with itself.
Original entry on oeis.org
4, 94, 455, 539, 994, 7665, 9994, 72721, 99994, 356429, 643565, 999994, 9090910, 9999994, 35294118, 64705876, 99999994, 335664329, 664335665, 684210520, 818181819, 838056674, 846153847, 866028702, 980125139, 999999994
Offset: 1
-
q:= proc(d,m) local R,t,a,b,x,q;
t:= 10^d+1;
R:= NULL;
for a in numtheory:-divisors(t) do
b:= t/a;
if igcd(a,b) > 1 then next fi;
for x from chrem([0,-m],[a,b]) by t do
q:= x*(x+m)/t;
if q >= 10^d then break fi;
if q >= 10^(d-1) then R:= R, x fi;
od od;
sort(convert({R},list));
end proc:
[seq(op(q(d,7)),d=1..10)]; # Robert Israel, Apr 09 2025
A116152
Numbers k such that k concatenated with k-1 gives the product of two numbers which differ by 7.
Original entry on oeis.org
9, 11, 45, 18281, 32769, 56891, 180689, 330539, 959481, 1850201, 3247409, 4940219, 2425563239, 2575561739, 6003563495, 7245212645, 7770160145, 4983798265289, 5049762270381, 5534298528989, 5603798594169
Offset: 1
A116269
Numbers k such that k*(k+7) gives the concatenation of two numbers m and m-3.
Original entry on oeis.org
87, 3675, 6319, 8785, 48742, 51252, 87616, 3762553, 6237441, 9217099, 3266298273, 3520463763, 6479536231, 6733701721, 8063694647, 8317860137, 4689524709430934473, 5310475290569065521, 7416797436703661746
Offset: 1
A116282
Numbers k such that k*(k+6) gives the concatenation of two numbers m and m-1.
Original entry on oeis.org
7744, 8018, 33294315, 66705680, 98000198, 340465755422, 476452552742, 523547447253, 659534244573, 866013200678, 998000001998, 3695104677080131, 3755782995538765, 4198081170077528, 4803478892324963, 5196521107675032
Offset: 1
98000198 * 98000204 = 96040393//96040392, where // denotes concatenation.
A116284
n times n+9 gives the concatenation of two numbers m and m-1.
Original entry on oeis.org
32, 60, 804, 4778, 5214, 7406, 48208886, 51791106, 77620651, 4291816088, 4482541430, 5517458562, 5708183904, 9036996876, 9737360643, 3579205562000136225339579331, 3939042613182345526485238179
Offset: 1
Showing 1-5 of 5 results.
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