A116345 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m+8.

41, 54, 40354308, 59645687, 39704957106129738595969799927611, 44505281604832422780051712184760, 45053875613995255103944518907120, 54946124386004744896055481092875, 55494718395167577219948287815235, 60295042893870261404030200072384, 68683652917306421895276391964227

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Examples

			59645687 * 59645693 = 35576083//35576091, where // denotes concatenation.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..41

Crossrefs

Cf. A116168, A116339, A116344, A116346, A116352.

Programs

Maple

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

Extensions

More terms from Robert Israel, Jan 17 2017