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

1,3

Comments

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

Links

Table of n, a(n) for n=1..14.

Formula

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

Prog

(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
(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

Crossrefs

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

Sequence in context: A159359 A119864 A036240 * A355127 A292056 A277311

Adjacent sequences: A346506 A346507 A346508 * A346510 A346511 A346512

Keyword

nonn,base,hard,more

Author

Stefano Spezia, Jul 21 2021

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

Status

approved