A116180
Numbers k such that k concatenated with k+3 gives the product of two numbers which differ by 7.
Original entry on oeis.org
7137, 7767, 47783068991048776635, 48797525371338932241, 55658688122404752991, 56753136503494828605, 85555875266989354735, 86911515887391841491, 95992713077544748491, 97428345698747155255
Offset: 1
7767//7770 = 8810 * 8817, where // denotes concatenation.
7767//7762 = 8809 * 8818.
7767//7776 = 8811 * 8816.
A116207
Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 5.
Original entry on oeis.org
493, 607, 629, 757, 17927, 33247, 93869, 19467217, 31223879, 72757727, 13454739732766891651472740499, 40093333713615672956030023507, 48089152118689474641229584727, 66424317743191484432891678269
Offset: 1
72757727//72757734 = 85298138 * 85298143, where // denotes concatenation.
-
f:= proc(d) # terms where k+7 has d digits
local S,x,R,k;
S:= map(t -> rhs(op(t)), [msolve(x*(x+5) = 7, 10^d+1)]);
R:= NULL:
for x in S do
k := (x*(x+5)-7)/(10^d+1);
if ilog10(k+7) = d - 1 then R:= R,k fi
od:
op(sort([R]))
end proc:
map(f, [$1..31]); # Robert Israel, Nov 27 2024
A116113
Numbers k such that k concatenated with k-7 gives the product of two numbers which differ by 8.
Original entry on oeis.org
95, 216, 287, 515, 675, 995, 1175, 4320, 9995, 82640, 99995, 960795, 999995, 1322312, 4049591, 9999995, 16955015, 34602080, 99999995, 171010235, 181964891, 183673467, 187160072, 321920055, 326530616, 328818032
Offset: 1
8533818720//8533818713 = 9237867023 * 9237867031, where // denotes concatenation.
A116109
Numbers k such that k concatenated with k-8 gives the product of two numbers which differ by 9.
Original entry on oeis.org
94, 210, 294, 994, 5880, 9994, 52888, 99994, 127044, 414180, 999994, 8264470, 9999994, 12456750, 41868508, 99999994, 112670544, 441341880, 468144040, 669421494, 702338994, 715976338, 750005718, 960645294, 999999994
Offset: 1
8505429358//8505429350 = 9222488466 * 9222488475, where // denotes concatenation.
A116245
n times n+9 gives the concatenation of two numbers m and m-7.
Original entry on oeis.org
8, 698, 775, 789, 866, 42336, 57656, 96882, 44121665, 55878327, 85298136, 36680703009575609347721358492, 63319296990424390652278641500, 69346342454876071597336150480, 81501115172242572470460459682
Offset: 1
85298136 * 85298145 = 72757727//72757720, where // denotes
concatenation.
Showing 1-5 of 5 results.
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