A116168
Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 8.
Original entry on oeis.org
19, 32, 16284704, 35576083, 15764836187996024260119639732979, 19807200907254352332962649366152, 20298517078413563250826300137112, 30190765850423053042937262322867, 30796637697589506772859224996627
Offset: 1
35576083//35576084 = 59645686 * 59645694, where // denotes concatenation.
35576083//35576091 = 59645687 * 59645693.
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
A116339
k times k+6 gives the concatenation of two numbers m and m+7.
Original entry on oeis.org
378, 617, 708, 903, 8761, 45456, 54539, 693063, 8181812, 88235288, 327935224, 330669332, 363636365, 418318517, 428571430, 461538455, 538461540, 571428565, 581681478, 636363630, 669330663, 672064771, 691571588
Offset: 1
-
f:= proc(d) local S,x;
S:= map(rhs@op,[msolve((x+3)^2 = 16, 10^d+1)]);
end proc:
g:= proc(n,d) local m; m:= ((n+3)^2-16)/(10^d+1)+7; m >= 10^(d-1) and m < 10^d end proc:
sort([seq](op(select(g,f(i),i)),i=2..13)); # Robert Israel, Jan 27 2024
A116194
Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 6.
Original entry on oeis.org
1, 2, 10, 47, 550, 802, 570035, 623387, 1327222, 4041011, 8252210, 164398539591831062, 173868055738777586, 339918283297349107, 353476744122425611, 846974882088186070, 868300386379144450
Offset: 1
8252210//8252215 = 9084165 * 9084171, where // denotes
concatenation.
A116209
Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 7.
Original entry on oeis.org
1, 13, 41, 653, 2287, 2723, 5491, 23240971, 26823191, 60249661, 1841968537, 2009317771, 3044234903, 3258336353, 8166731261, 9481619237, 1281071245505271100098621541, 1551605670846640136726379653
Offset: 1
Showing 1-5 of 5 results.
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