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A347749 Number of positive integers with n digits and final digit 6 that are equal to the product of two integers ending with the same digit. 2
0, 4, 33, 352, 3597, 36781, 374071, 3790993, 38326689, 386782889 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the number of n-digit numbers in A347747.

LINKS

Table of n, a(n) for n=1..10.

FORMULA

a(n) < A052268(n).

a(n) = A337856(n) + A347255(n) - A347748(n).

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

MATHEMATICA

Table[{lo, hi}={10^(n-1), 10^n}; Length@Select[Union[Union@Flatten@Table[a*b, {a, 4, Floor[hi/4], 10}, {b, a, Floor[hi/a], 10}], Union@Flatten@Table[a*b, {a, 6, Floor[hi/6], 10}, {b, a, Floor[hi/a], 10}]], lo<#<hi&], {n, 8}]

PROG

(Python)

def a(n):

lo, hi = 10**(n-1), 10**n

return len(set(a*b for a in range(4, hi//4+1, 10) for b in range(a, hi//a+1, 10) if lo <= a*b < hi) | set(a*b for a in range(6, hi//6+1, 10) for b in range(a, hi//a+1, 10) if lo <= a*b < hi))

print([a(n) for n in range(1, 9)]) # Michael S. Branicky, Oct 06 2021

CROSSREFS

Cf. A017341, A052268, A324297, A337856, A347253, A347255, A347747, A347748.

Sequence in context: A093185 A198006 A339654 * A075132 A303919 A208961

Adjacent sequences: A347746 A347747 A347748 * A347750 A347751 A347752

KEYWORD

nonn,base,hard,more

AUTHOR

Stefano Spezia, Sep 12 2021

EXTENSIONS

a(9)-a(10) from Michael S. Branicky, Oct 06 2021

STATUS

approved

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Last modified February 4 23:12 EST 2023. Contains 360082 sequences. (Running on oeis4.)