A116202
Numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 8.
Original entry on oeis.org
7, 54, 234, 267, 894, 58227, 7962242238271227055830015496107, 60153956829051761181170060654114714579377214308482459, 2019668016997743800626449453386765007975459365956534868322001037107, 3031524678136833532602149525055953135725227119574025423809994922862
Offset: 1
58227//58233 = 76303 * 76311, where // denotes concatenation.
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from itertools import count, islice
from sympy import sqrt_mod
def A116202_gen(): # generator of terms
for j in count(0):
b = 10**j
a = b*10+1
for k in sorted(sqrt_mod(22,a,all_roots=True)):
if a*(b-6) <= k**2-22 < a*(a-7) and k>4:
yield (k**2-22)//a
A116202_list = list(islice(A116202_gen(),7)) # Chai Wah Wu, Feb 21 2024
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
A116195
Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 7.
Original entry on oeis.org
7403, 8885, 12563, 41675, 54239, 2353623, 2650793, 7717533, 527390351115, 567933643889, 627121279653, 671264212463, 1335723019653517755, 2049430589972661489, 2995303155542192885, 4026214090447622723
Offset: 1
7717533//7717538 = 8784946 * 8784953, 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.
-
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
A116197
Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 9.
Original entry on oeis.org
25, 2448207281, 2552334847, 9492271895, 10713024775597019390267617, 45251510049471045364918031, 99414584492459886818648287, 1000584180267191789271991959007645
Offset: 1
Showing 1-5 of 5 results.