A346509 Number of positive integers with n digits that are the product of two integers greater than 1 and ending with 1.

0, 0, 12, 200, 2660, 31850, 361985, 3982799, 42914655, 455727689, 4788989458, 49930700093, 517443017072, 5336861879564

Offset: 1

Author

Stefano Spezia, Jul 21 2021

Keywords

• nonn
• base
• hard
• more

Comments

a(n) is the number of n-digit numbers in A346507.

Crossrefs

Cf. A017281, A052268, A087630, A337855 (ending with 5), A337856 (ending with 6), A346507.

Programs

PARI

a(n) = {my(res = 0); forstep(i = 10^(n-1) + 1, 10^n, 10, f = factor(i); if(bigomega(f) == 1, next); d = divisors(f); for(j = 2, (#d~ + 1)>>1, if(d[j]%10 == 1 && d[#d + 1 - j]%10 == 1, res++; next(2) ) ) ); res } \\ David A. Corneth, Jul 22 2021

Python

def A346507upto(lim): return sorted(set(a*b for a in range(11, lim//11+1, 10) for b in range(a, lim//a+1, 10)))
def a(n): return len(A346507upto(10**n)) - len(A346507upto(10**(n-1)))
print([a(n) for n in range(1, 9)]) # Michael S. Branicky, Jul 22 2021

Formula

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

Extensions

a(6)-a(9) from Michael S. Branicky, Jul 22 2021

a(10) from David A. Corneth, Jul 22 2021

a(11) from Michael S. Branicky, Jul 23 2021

a(11) corrected and extended with a(12) by Martin Ehrenstein, Aug 03 2021

a(13)-a(14) from Martin Ehrenstein, Aug 05 2021