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A116196
Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 8.
5
68, 12585135, 17104748, 34388975, 41634068, 1100788419388203283323, 1415702077730399453204, 1615864923864298764860, 1993221328488651223275, 3064119854121476750348, 3576300448435797632079, 3890538749986876109435
OFFSET
1,1
EXAMPLE
41634068//41634073 = 64524463 * 64524471, where // denotes concatenation.
PROG
(Python)
from itertools import count, islice
from sympy import sqrt_mod
def A116196_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**2-21)//a
A116196_list = list(islice(A116196_gen(), 10)) # Chai Wah Wu, Feb 21 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Giovanni Resta, Feb 06 2006
STATUS
approved