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.
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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
A116203
Numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 9.
Original entry on oeis.org
24, 26, 1014, 1196, 4280, 4646, 10512559797957763880, 22117246687805424846, 24058546574769555806, 25959521962351403984, 28059292876752476030, 45666404019969616806, 51120259070514684854, 56575813788698035286
Offset: 1
4646//4652 = 6812 * 6821, where // denotes concatenation.
A116328
n times n+9 gives the concatenation of two numbers m and m+5.
Original entry on oeis.org
46, 4947936213, 5052063779, 9742829100, 32730757363062987012674789, 67269242636937012987325203, 99706862598549297056423092, 3163201195414530993427385140698350
Offset: 1
Showing 1-4 of 4 results.