A115430
Numbers k such that the concatenation of k with k+9 gives a square.
Original entry on oeis.org
216, 287, 515, 675, 1175, 4320, 82640, 960795, 1322312, 4049591, 16955015, 34602080, 171010235, 181964891, 183673467, 187160072, 321920055, 326530616, 328818032, 343942560, 470954312, 526023432, 528925616, 534830855
Offset: 1
Cf.
A030465,
A102567,
A115426,
A115437,
A115428,
A115429,
A115431,
A115432,
A115433,
A115434,
A115435,
A115436,
A115441.
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
A116335
Numbers k such that k*(k+2) gives the concatenation of two numbers m and m+7.
Original entry on oeis.org
7746, 8020, 33294317, 66705682, 98000200, 340465755424, 476452552744, 523547447255, 659534244575, 866013200680, 998000002000, 3695104677080133, 3755782995538767, 4198081170077530, 4803478892324965, 5196521107675034
Offset: 1
98000200 * 98000202 = 96040393//96040400, where // denotes concatenation.
A116343
Numbers k such that k*(k+1) gives the concatenation of two numbers m and m+8.
Original entry on oeis.org
14, 86, 76983, 714690, 952314, 90438191, 96320544, 32980078899029, 34346653774238, 42816188292273, 42881990066488, 57118009933512, 57183811707727, 65653346225762, 67019921100971, 81321742742210
Offset: 1
96320544 * 96320545 = 92776472//92776480, where // denotes concatenation.
Showing 1-4 of 4 results.
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