A116133
Numbers k such that k concatenated with k-4 gives the product of two numbers which differ by 9.
Original entry on oeis.org
64, 1876, 3214, 8776, 17227120144584448354, 19391087990479091186, 21557280540171744040, 23970390649400564404, 26051259424903756364, 28697643366269876506, 31320461807899711990, 34215988012600009664
Offset: 1
8776//8772 = 9364 * 9373, where // denotes concatenation. Also 8776//8780 = 9365 * 9372.
A116320
n times n+8 gives the concatenation of two numbers m and m+4.
Original entry on oeis.org
4, 86, 32762, 67231, 76322, 693956, 900097, 7295105, 9068525, 3664355432, 6335644561, 8015841979, 8419801579, 9900000997, 3252382148828, 6747617851165, 7253863787097, 9474890578438, 9981136514370
Offset: 1
-
Res:= NULL: count:= 0:
for d from 1 while count < 100 do
R:= sort(select(t -> t^2 + 8*t - 4 > 10^(2*d-1) and t^2+8*t-4 < 10^(2*d), map(t -> rhs(op(t)), [msolve(n^2+8*n-4, 10^d+1)])));
count := count+nops(R);
Res:= Res, op(R);
od:
Res; # Robert Israel, Jun 20 2018
A116181
Numbers k such that k concatenated with k+3 gives the product of two numbers which differ by 8.
Original entry on oeis.org
57, 1062, 4545, 9517, 65040816823705919148274557212824575357, 73854453524198329292125744115286819630, 78444109191135472482770868099397646205
Offset: 1
9517//9520 = 9752 * 9760, where // denotes concatenation.
A116196
Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 8.
Original entry on oeis.org
68, 12585135, 17104748, 34388975, 41634068, 1100788419388203283323, 1415702077730399453204, 1615864923864298764860, 1993221328488651223275, 3064119854121476750348, 3576300448435797632079, 3890538749986876109435
Offset: 1
41634068//41634073 = 64524463 * 64524471, where // denotes concatenation.
-
from itertools import count, islice
from sympy import sqrt_mod
def A116196_gen(): # generator of terms
for j in count(0):
b = 10**j
a = b*10+1
for k in sorted(sqrt_mod(21,a,all_roots=True)):
if a*(b-5) <= k**2-21 < a*(a-6) and k>4:
yield (k**2-21)//a
A116196_list = list(islice(A116196_gen(),10)) # Chai Wah Wu, Feb 21 2024
A116190
Numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 9.
Original entry on oeis.org
16, 36, 12366, 42036, 64996, 1589736168, 1921234732, 3154856388, 3615437032, 5939192968, 6565302732, 1888656611704713276, 2251541774559900786, 2761459004510103616, 3196921199936328628, 63080834574071218603723158
Offset: 1
Showing 1-5 of 5 results.
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