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
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
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.
A116334
n times n+9 gives the concatenation of two numbers m and m+6.
Original entry on oeis.org
45, 47, 3180, 3454, 6538, 6812, 32423077888994073533, 47028976905526474404, 49049512306209075907, 50950487693790924085, 52971023094473525588, 67576922111005926459, 71498432899270376140, 75216895567882908524
Offset: 1
6812 * 6821 = 4646//4652, where // denotes concatenation.
Showing 1-5 of 5 results.