A116169
Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 9.
Original entry on oeis.org
9, 49, 1166975893986638437392162264780939, 1411174268292962563778302427727571, 1860631503683565562655236868895135
Offset: 1
49//50 = 66 * 75, where // denotes concatenation.
49//58 = 67 * 74.
A116210
Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 8.
Original entry on oeis.org
73, 101, 466, 577, 913, 938, 1027699544347561123497066503878337002, 1043891904746431592729642732987859418, 1406975496023772119400647610836667853, 3905041089422306453928649115284570106, 4582028691256280367677282506239892877, 4616148891509946292221374856300250093
Offset: 1
938//945 = 965 * 973, where // denotes concatenation.
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from itertools import count, islice
from sympy import sqrt_mod
def A116210_gen(): # generator of terms
for j in count(0):
b = 10**j
a = b*10+1
for k in sorted(sqrt_mod(23,a,all_roots=True)):
if a*(b-7) <= k**2-23 < a*(a-8) and k>4:
yield (k**2-23)//a
A116210_list = list(islice(A116210_gen(),10)) # Chai Wah Wu, Feb 22 2024
A116354
n times n+8 gives the concatenation of two numbers m and m+9.
Original entry on oeis.org
365, 628, 771, 859, 9043, 81820, 366328, 633665, 7272729, 35294109, 64705884, 336663328, 340080963, 377622379, 400178770, 454545456, 477101847, 522898146, 545454537, 599821223, 622377614, 659919030, 663336665
Offset: 1
A116224
Numbers k such that k concatenated with k+9 gives the product of two numbers which differ by 9.
Original entry on oeis.org
23, 27, 10357253, 10577583, 45531191, 45991881, 12823841629508531559818193, 17153953024599261169512903, 34319291138166088695725681, 41203057971387248588060861, 75861857890090990570762781
Offset: 1
45991881//45991890 = 67817310 * 67817319, where // denotes concatenation.
Showing 1-4 of 4 results.
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