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Number of positive integers with n digits that are the product of two integers ending with 6.
12

%I #28 Sep 26 2021 10:36:59

%S 0,2,20,230,2515,26889,282211,2930013,30196730,309564822,3161099901,

%T 32182595954,326874672928,3313770788984

%N Number of positive integers with n digits that are the product of two integers ending with 6.

%C a(n) is the number of n-digit numbers in A324297.

%H <a href="/index/Di#digits">Index entries for sequences related to digits</a>.

%F Conjecture: Lim_{n->infinity} a(n)/a(n-1) = 10.

%o (Python)

%o def A337856(n):

%o k, n1, n2, pset = 0, 10**(n-1)//2-18, 10**n//2-18, set()

%o while 50*k**2+60*k < n2:

%o a, b = divmod(n1-30*k,50*k+30)

%o m = max(k,a+int(b>0))

%o r = 50*k*m+30*(k+m)

%o while r < n2:

%o pset.add(r)

%o m += 1

%o r += 50*k+30

%o k += 1

%o return len(pset) # _Chai Wah Wu_, Sep 26 2021

%Y Cf. A017341, A324297, A337855, A346509.

%K nonn,base,hard,more

%O 1,2

%A _Stefano Spezia_, Sep 27 2020

%E a(5) corrected by and a(6)-a(9) from _Jinyuan Wang_, Oct 01 2020

%E a(10)-a(13) from _Bert Dobbelaere_, Oct 20 2020

%E a(14) from _Martin Ehrenstein_, Aug 06 2021