A346510 -id:A346510 - cp's OEIS frontend

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

Stefano Spezia, Jul 21 2021

All the terms end with 1 (A017281).

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

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

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

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

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

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

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

A346508 Positive integers k such that 10*k+1 is equal to the product of two integers greater than 1 and ending with 1 (A346507).

Original entry on oeis.org

12, 23, 34, 44, 45, 56, 65, 67, 78, 86, 89, 96, 100, 107, 111, 122, 127, 128, 133, 144, 149, 155, 158, 166, 168, 170, 177, 188, 189, 191, 199, 209, 210, 212, 220, 221, 232, 233, 243, 250, 251, 254, 260, 265, 275, 276, 282, 287, 291, 296, 298, 309, 311, 313, 317

Offset: 1

Stefano Spezia, Jul 21 2021

			107 is a term because 21*51 = 1071 = 107*10 + 1.

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

Cf. A016873 (ending with 5), A017281, A324298 (ending with 6), A346507, A346509, A346510.

a={}; For[n=1, n<=350, n++, For[k=1, kMax[10a+1], AppendTo[a, n]]]]; a

def aupto(lim): return sorted(set(a*b//10 for a in range(11, 10*lim//11+2, 10) for b in range(a, 10*lim//a+2, 10) if a*b//10 <= lim))
print(aupto(318)) # Michael S. Branicky, Aug 21 2021

a(n) = (A346507(n) - 1)/10.
Conjecture: lim_{n->infinity} a(n)/a(n-1) = 1.
The conjecture is true since a(n) = (A346507(n) - 1)/10 and lim_{n->infinity} A346507(n)/A346507(n-1) = 1. - Stefano Spezia, Aug 21 2021

cp's OEIS Frontend

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

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