A116333
k times k+8 gives the concatenation of two numbers m and m+6.
Original entry on oeis.org
23, 70, 480, 513, 942, 76303, 8923139715521228493004072379869, 77558981961505761619171327422086381910161500424346805, 4494071669430455134012149964165405936125116123191254722256003057119, 5505928330569544865987850035834594063874883876808745277743996942874
Offset: 1
76303 * 76311 = 58227//58233, where // denotes concatenation, so 76303 is a term.
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from itertools import count, islice
from sympy import sqrt_mod
def A116333_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-4
A116333_list = list(islice(A116333_gen(),10)) # Chai Wah Wu, Feb 21 2024
A116210
Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 8.
Original entry on oeis.org
73, 101, 466, 577, 913, 938, 1027699544347561123497066503878337002, 1043891904746431592729642732987859418, 1406975496023772119400647610836667853, 3905041089422306453928649115284570106, 4582028691256280367677282506239892877, 4616148891509946292221374856300250093
Offset: 1
938//945 = 965 * 973, where // denotes concatenation.
-
from itertools import count, islice
from sympy import sqrt_mod
def A116210_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**2-23)//a
A116210_list = list(islice(A116210_gen(),10)) # Chai Wah Wu, Feb 22 2024
A116340
n times n+7 gives the concatenation of two numbers m and m+7.
Original entry on oeis.org
2, 33, 61, 805, 4779, 5215, 7407, 48208887, 51791107, 77620652, 4291816089, 4482541431, 5517458563, 5708183905, 9036996877, 9737360644, 3579205562000136225339579332, 3939042613182345526485238180
Offset: 1
A116342
n times n+9 gives the concatenation of two numbers m and m+7.
Original entry on oeis.org
4415, 5577, 7840, 3188375836088211088457055570, 4940200653606459263639537322, 5059799346393540736360462670, 6811624163911788911542944422, 6977607565571622928141284588
Offset: 1
7840 * 7849 = 6153//6160, where // denotes concatenation.
A116354
n times n+8 gives the concatenation of two numbers m and m+9.
Original entry on oeis.org
365, 628, 771, 859, 9043, 81820, 366328, 633665, 7272729, 35294109, 64705884, 336663328, 340080963, 377622379, 400178770, 454545456, 477101847, 522898146, 545454537, 599821223, 622377614, 659919030, 663336665
Offset: 1
Showing 1-5 of 5 results.