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.
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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
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.
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.
A116347
n times n+9 gives the concatenation of two numbers m and m+8.
Original entry on oeis.org
345, 647, 829, 878, 933, 33180, 42271, 57721, 66812, 316429537030539, 319485532390187, 328611858418903, 332707864512186, 339600869407914, 347417506407134, 355879196889561, 370588838784509, 383811170906508
Offset: 1
66812 * 66821 = 44644//44652, where // denotes concatenation.
Showing 1-4 of 4 results.