A116174
Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 8.
Original entry on oeis.org
1143, 4382, 4943, 24941511, 25058558, 94090583, 616729341438, 638432642423, 978717194478, 994009005983, 1636200161363007, 1710661666314798, 1805005185949007, 1906479843038783, 1986790648039982, 3072104679280383
Offset: 1
94090583//94090585 = 97000297 * 97000305, where // denotes concatenation.
94090583//94090592 = 97000298 * 97000304.
A116345
Numbers k such that k*(k+6) gives the concatenation of two numbers m and m+8.
Original entry on oeis.org
41, 54, 40354308, 59645687, 39704957106129738595969799927611, 44505281604832422780051712184760, 45053875613995255103944518907120, 54946124386004744896055481092875, 55494718395167577219948287815235, 60295042893870261404030200072384, 68683652917306421895276391964227
Offset: 1
59645687 * 59645693 = 35576083//35576091, where // denotes concatenation.
-
f:= proc(d) local R;
R:= map(rhs@op,{msolve(x^2=17,10^d+1)});
R:= map(t -> (t-3) mod (10^d+1), R);
op(select(proc(t) local m; m:= (t*(t+6)-8)/(10^d+1)+8; m >= 10^(d-1) and m < 10^d end proc, R));
end proc;
sort(convert({seq(f(i),i=1..50)},list)); # Robert Israel, Jan 17 2017
A116351
Numbers k such that k*(k+5) gives the concatenation of two numbers m and m+9.
Original entry on oeis.org
8446, 8811, 69125298546226023972, 69855225553525294045, 74604750601020544520, 75334677608319814593, 92496418993920707747, 93226346001219977820, 97975871048715228295, 98705798056014498368
Offset: 1
8811 * 8816 = 7767//7776, where // denotes concatenation.
A116353
Numbers k such that k*(k+7) gives the concatenation of two numbers m and m+9.
Original entry on oeis.org
27, 67, 3416102887775247376839416334668636, 3756559953325598880263233435801765, 4313503800489302411917772257282209
Offset: 1
67 * 74 = 49//58, where // denotes concatenation.
Showing 1-4 of 4 results.
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