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
A116208
Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 6.
Original entry on oeis.org
145, 384, 505, 820, 7680, 20665, 29748, 480340, 6694209, 77854665, 107541513, 109342209, 132231408, 174990384, 183673473, 213017748, 289940833, 326530608, 338353345, 404958673, 448003540, 451671060, 478271265
Offset: 1
A116325
n times n+6 gives the concatenation of two numbers m and m+5.
Original entry on oeis.org
2, 3, 29, 66, 739, 893, 755004, 789546, 3643103, 6356892, 9084165, 405460897734702723, 416974886220714237, 583025113779285758, 594539102265297272, 920312382883217575, 931826371369229089
Offset: 1
9084165 * 9084171 = 8252210//8252215, where // denotes
concatenation.
A116338
n times n+5 gives the concatenation of two numbers m and m+7.
Original entry on oeis.org
700, 777, 791, 868, 42338, 57658, 96884, 44121667, 55878329, 85298138, 36680703009575609347721358494, 63319296990424390652278641502, 69346342454876071597336150482, 81501115172242572470460459684
Offset: 1
85298138 * 85298143 = 72757727//72757734, where // denotes
concatenation.
A116340
n times n+7 gives the concatenation of two numbers m and m+7.
Original entry on oeis.org
2, 33, 61, 805, 4779, 5215, 7407, 48208887, 51791107, 77620652, 4291816089, 4482541431, 5517458563, 5708183905, 9036996877, 9737360644, 3579205562000136225339579332, 3939042613182345526485238180
Offset: 1
Showing 1-5 of 5 results.