A346507 Positive integers k that are the product of two integers greater than 1 and ending with 1.

121, 231, 341, 441, 451, 561, 651, 671, 781, 861, 891, 961, 1001, 1071, 1111, 1221, 1271, 1281, 1331, 1441, 1491, 1551, 1581, 1661, 1681, 1701, 1771, 1881, 1891, 1911, 1991, 2091, 2101, 2121, 2201, 2211, 2321, 2331, 2431, 2501, 2511, 2541, 2601, 2651, 2751, 2761

Offset: 1

Author

Stefano Spezia, Jul 21 2021

Keywords

• nonn
• base

Comments

All the terms end with 1 (A017281).

Examples

			121 = 11*11, 231 = 11*21, 341 = 11*31, 441 = 21*21, 451 = 11*41, ...
		

Links

• Stefano Spezia, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A017281 (supersequence), A053742 (ending with 5), A324297 (ending with 6), A346508, A346509, A346510.

Programs

Mathematica

a={}; For[n=1, n<=300, n++, For[k=1, kMax[a], AppendTo[a, 10n+1]]]]; a

PARI

isok(k) = fordiv(k, d, if ((d>1) && (dMichel Marcus, Jul 28 2021

Python

def aupto(lim): return sorted(set(a*b for a in range(11, lim//11+1, 10) for b in range(a, lim//a+1, 10)))
print(aupto(2761)) # Michael S. Branicky, Jul 22 2021

Formula

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

The conjecture is true since it can be proved that a(n) = (sqrt(a(n-1)) + g(n-1))^2 where [g(n): n > 1] is a bounded sequence of positive real numbers. - Stefano Spezia, Aug 21 2021