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
A116331
n times n+5 gives the concatenation of two numbers m and m+6.
Original entry on oeis.org
456, 540, 7666, 72722, 356430, 643566, 9090911, 35294119, 64705877, 335664330, 664335666, 684210521, 818181820, 838056675, 846153848, 866028703, 980125140, 3861386140, 6138613856, 6916125390, 9222488468, 41358246491
Offset: 1
A116337
Numbers k such that k*(k+4) gives the concatenation of two numbers m and m+7.
Original entry on oeis.org
8217108, 8030443878983905982, 43467818511541680701794365325328847002052, 56532181488458319298205634674671152997945
Offset: 1
8217108 * 8217112 = 6752089//6752096, where // denotes concatenation.
A116351
Numbers k such that k*(k+5) gives the concatenation of two numbers m and m+9.
Original entry on oeis.org
8446, 8811, 69125298546226023972, 69855225553525294045, 74604750601020544520, 75334677608319814593, 92496418993920707747, 93226346001219977820, 97975871048715228295, 98705798056014498368
Offset: 1
8811 * 8816 = 7767//7776, where // denotes concatenation.
Showing 1-5 of 5 results.
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