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
A116341
k times k+8 gives the concatenation of two numbers m and m+7.
Original entry on oeis.org
82, 314, 679, 756, 952, 965, 3205775326418807415637845823789043451, 3230931606745075612526180113373983267, 3750967203300732832735999247776048870, 6249032796699267167264000752223951123, 6769068393254924387473819886626016726, 6794224673581192584362154176210956542
Offset: 1
965 * 973 = 938//945, where // denotes concatenation, so 965 is a term.
-
from itertools import count, islice
from sympy import sqrt_mod
def A116341_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-4
A116341_list = list(islice(A116341_gen(),20)) # Chai Wah Wu, Feb 21 2024
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
A116211
Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 9.
Original entry on oeis.org
1953, 3115, 6153, 1016574047215119910181525023, 2440558249789368730986767575, 2560156942576450203707692923, 4639822375038697733267413875, 4868700733912235016077891029
Offset: 1
6153//6160 = 7840 * 7849, where // denotes concatenation.
A116223
Numbers k such that k concatenated with k+9 gives the product of two numbers which differ by 8.
Original entry on oeis.org
136, 399, 600, 744, 8184, 66951, 134199, 401536, 5289264, 12456744, 41868519, 113342199, 115655064, 142598664, 160143051, 206611575, 227626176, 273422475, 297520656, 359785504, 387353899, 435493131, 440015536
Offset: 1
Showing 1-5 of 5 results.