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
A116203
Numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 9.
Original entry on oeis.org
24, 26, 1014, 1196, 4280, 4646, 10512559797957763880, 22117246687805424846, 24058546574769555806, 25959521962351403984, 28059292876752476030, 45666404019969616806, 51120259070514684854, 56575813788698035286
Offset: 1
4646//4652 = 6812 * 6821, where // denotes concatenation.
A116328
n times n+9 gives the concatenation of two numbers m and m+5.
Original entry on oeis.org
46, 4947936213, 5052063779, 9742829100, 32730757363062987012674789, 67269242636937012987325203, 99706862598549297056423092, 3163201195414530993427385140698350
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.
Showing 1-4 of 4 results.