A116189
Numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 8.
Original entry on oeis.org
4, 80, 10736, 45205, 58256, 481580, 810181, 5321861, 8223821, 1342750076, 4014039205, 6425372269, 7089305869, 9801001981, 1057798964204, 4553034666541, 5261853984181, 8977355147344, 9962308611856
Offset: 1
A116312
n times n+8 gives the concatenation of two numbers m and m+3.
Original entry on oeis.org
72, 3255, 6738, 9752, 80647887029795095027968358511096470120, 85938613861405938604061385940594061403, 88568679109003015820047566431888549328
Offset: 1
9752 * 9760 = 9517//9520, where // denotes concatenation.
A116319
n times n+7 gives the concatenation of two numbers m and m+4.
Original entry on oeis.org
77, 4328, 5666, 9365, 41505566065992219342, 44035313091289689595, 46429818586950933764, 48959565612248404017, 51040434387751595977, 53570181413049066230, 55964686908710310399, 58494433934007780652
Offset: 1
9365 * 9372 = 8776//8780, where // denotes concatenation.
A116327
k times k+8 gives the concatenation of two numbers m and m+5.
Original entry on oeis.org
79, 35475530, 41357883, 58642110, 64524463, 3317813164402425001808, 3762581663871761671881, 4019782237714250566387, 4464550737183587236460, 5535449262816412763533, 5980217762285749433606, 6237418336128238328112
Offset: 1
64524463 * 64524471 = 41634068//41634073, where // denotes concatenation, so 64524463 is a term.
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from itertools import count, islice
from sympy import sqrt_mod
def A116327_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-4
A116327_list = list(islice(A116327_gen(),20)) # Chai Wah Wu, Feb 21 2024
A116321
n times n+9 gives the concatenation of two numbers m and m+4.
Original entry on oeis.org
36, 56, 35161, 64831, 80616, 3987149564, 4383189168, 5616810824, 6012850428, 7706615964, 8102655568, 4345867705884192320, 4745041385024898581, 5254958614975101411, 5654132294115807672, 79423444003688998051750982
Offset: 1
Showing 1-5 of 5 results.