A116275
Numbers k such that k*(k+4) gives the concatenation of two numbers m and m-2.
Original entry on oeis.org
8872, 9009, 83352840, 99000099, 329767122286, 670232877711, 738226276371, 933006600339, 999000000999, 3779410975143113, 3872816717528065, 4250291784692548, 4278630943941865, 4372036686326817, 4749511753491300, 5250488246508697, 5627963313673180, 5721369056058132
Offset: 1
99000099 * 99000103 = 98010199//98010197, where // denotes concatenation.
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from itertools import count, islice
from sympy import sqrt_mod
def A116275_gen(): # generator of terms
for j in count(0):
b = 10**j
a = b*10+1
for k in sorted(sqrt_mod(2,a,all_roots=True)):
if a*(b+3) <= k**2-2 < a*(a+2):
yield k-2
A116275_list = list(islice(A116275_gen(),30)) # Chai Wah Wu, Feb 19 2024
A116280
n times n+3 gives the concatenation of two numbers m and m-1.
Original entry on oeis.org
6, 77, 80918, 91808, 326509, 475024, 524974, 673489, 4323776, 4767131, 5232867, 5676222, 4083911140, 4975000249, 5024999749, 5916088858, 9503960495, 9604950395, 4186904462791, 4313465946774, 5686534053224, 5813095537207
Offset: 1
A116143
Numbers k such that k concatenated with k-2 gives the product of two numbers which differ by 3.
Original entry on oeis.org
10, 100, 132, 406, 510, 852, 1000, 7930, 10000, 66942, 100000, 113322, 440056, 1000000, 5289256, 10000000, 58477510, 100000000, 111333222, 164378892, 183673470, 200444410, 206611570, 224376732, 277008310, 297520662
Offset: 1
A116259
n times n+3 gives the concatenation of two numbers m and m-4.
Original entry on oeis.org
7282817, 8171727, 4550754022124826466, 5449245977875173532, 8176518705147900805, 8951999555715882882349355522888, 9861090464806791973258446431979
Offset: 1
8171727 * 8171730 = 6677714//6677710, where // denotes
concatenation.
A116273
Numbers k such that k*(k+2) gives the concatenation of two numbers m and m-2.
Original entry on oeis.org
90, 9078, 9900, 733673, 999000, 88225294, 99990000, 8900869207, 9296908811, 9604060396, 9999900000, 326666333266, 673333666733, 700730927007, 972603739726, 999999000000, 34519562953736, 39737862788837
Offset: 1
90 is a member since 90*92 = 8280 = 82 80.
9078 is a member since 9078*9080 = 82428240 = 8242 8240.
Showing 1-5 of 5 results.