A337856 Number of positive integers with n digits that are the product of two integers ending with 6.

0, 2, 20, 230, 2515, 26889, 282211, 2930013, 30196730, 309564822, 3161099901, 32182595954, 326874672928, 3313770788984

Offset: 1

Author

Stefano Spezia, Sep 27 2020

Keywords

• nonn
• base
• hard
• more

Comments

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

Links

• Index entries for sequences related to digits.

Crossrefs

Cf. A017341, A324297, A337855, A346509.

Programs

Python

def A337856(n):
    k, n1, n2, pset = 0, 10**(n-1)//2-18, 10**n//2-18, set()
    while 50*k**2+60*k < n2:
        a, b = divmod(n1-30*k,50*k+30)
        m = max(k,a+int(b>0))
        r = 50*k*m+30*(k+m)
        while r < n2:
            pset.add(r)
            m += 1
            r += 50*k+30
        k += 1
    return len(pset) # Chai Wah Wu, Sep 26 2021

Formula

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

Extensions

a(5) corrected by and a(6)-a(9) from Jinyuan Wang, Oct 01 2020

a(10)-a(13) from Bert Dobbelaere, Oct 20 2020

a(14) from Martin Ehrenstein, Aug 06 2021