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.
A116147
Numbers k such that k concatenated with k-2 gives the product of two numbers which differ by 9.
Original entry on oeis.org
4962, 237412345332, 262912791034, 468307643502
Offset: 1
4962//4960 = 7040 * 7049, where // denotes concatenation.
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.
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
A116326
Numbers k such that k*(k+7) gives the concatenation of two numbers m and m+5.
Original entry on oeis.org
8601, 9423, 35441, 64553, 73644, 4851412, 5148582, 8784946, 726216462985, 753613723259, 791909893642, 819307153916, 3654754464602947513, 4527063717215234299, 5472936282784765695, 6345245535397052481
Offset: 1
8784946 * 8784953 = 7717533//7717538, where // denotes concatenation.
Showing 1-5 of 5 results.
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