A116196 - OEIS

%I #13 Feb 22 2024 02:17:42

%S 68,12585135,17104748,34388975,41634068,1100788419388203283323,

%T 1415702077730399453204,1615864923864298764860,1993221328488651223275,

%U 3064119854121476750348,3576300448435797632079,3890538749986876109435

%N Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 8.

%e 41634068//41634073 = 64524463 * 64524471, where // denotes concatenation.

%o (Python)

%o from itertools import count, islice

%o from sympy import sqrt_mod

%o def A116196_gen(): # generator of terms

%o     for j in count(0):

%o         b = 10**j

%o         a = b*10+1

%o         for k in sorted(sqrt_mod(21,a,all_roots=True)):

%o             if a*(b-5) <= k**2-21 < a*(a-6) and k>4:

%o                 yield (k**2-21)//a

%o A116196_list = list(islice(A116196_gen(),10)) # _Chai Wah Wu_, Feb 21 2024

%Y Cf. A116189, A116195, A116197, A116202, A116327.

%K nonn,base

%O 1,1

%A _Giovanni Resta_, Feb 06 2006