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
A116146
Numbers k such that k concatenated with k-2 gives the product of two numbers which differ by 8.
Original entry on oeis.org
47, 550, 802, 570035, 623387, 1327222, 4041011, 8252210, 164398539591831062, 173868055738777586, 339918283297349107, 353476744122425611, 846974882088186070, 868300386379144450, 1875603455546506870
Offset: 1
8252210//8252208 = 9084164 * 9084172, where // denotes concatenation.
A116153
Numbers k such that k concatenated with k-1 gives the product of two numbers which differ by 9.
Original entry on oeis.org
13, 41, 653, 2287, 2723, 5491, 23240971, 26823191, 60249661, 1841968537, 2009317771, 3044234903, 3258336353, 8166731261, 9481619237, 1281071245505271100098621541, 1551605670846640136726379653
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.
A116200
Numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 5.
Original entry on oeis.org
210, 294, 5880, 52888, 127044, 414180, 8264470, 12456750, 41868508, 112670544, 441341880, 468144040, 669421494, 702338994, 715976338, 750005718, 960645294, 1491030294, 3768258010, 4783279044, 8505429358, 17105045530
Offset: 1
A116209
Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 7.
Original entry on oeis.org
1, 13, 41, 653, 2287, 2723, 5491, 23240971, 26823191, 60249661, 1841968537, 2009317771, 3044234903, 3258336353, 8166731261, 9481619237, 1281071245505271100098621541, 1551605670846640136726379653
Offset: 1
A116332
n times n+7 gives the concatenation of two numbers m and m+6.
Original entry on oeis.org
7041, 487249777146, 512750222848, 684330069117
Offset: 1
7041 * 7048 = 4962//4968, where // denotes concatenation.
A116140
Numbers k such that k concatenated with k-3 gives the product of two numbers which differ by 9.
Original entry on oeis.org
5, 7403, 8885, 12563, 41675, 54239, 2353623, 2650793, 7717533, 527390351115, 567933643889, 627121279653, 671264212463, 1335723019653517755, 2049430589972661489, 2995303155542192885, 4026214090447622723
Offset: 1
7717533//7717530 = 8784945 * 8784954, where // denotes concatenation.
A116278
n times n+9 gives the concatenation of two numbers m and m-2.
Original entry on oeis.org
7040, 487249777145, 512750222847, 684330069116
Offset: 1
7040 * 7049 = 4962//4960, where // denotes concatenation.
Showing 1-9 of 9 results.