(Translated by https://www.hiragana.jp/)
A346507 - OEIS
login
A346507
Positive integers k that are the product of two integers greater than 1 and ending with 1.
5
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
1,1
COMMENTS
All the terms end with 1 (A017281).
LINKS
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
EXAMPLE
121 = 11*11, 231 = 11*21, 341 = 11*31, 441 = 21*21, 451 = 11*41, ...
MATHEMATICA
a={}; For[n=1, n<=300, n++, For[k=1, k<n, k++, If[Mod[10n+1, 10k+1]==0 && Mod[(10n+1)/(10k+1), 10]==1 && 10n+1>Max[a], AppendTo[a, 10n+1]]]]; a
PROG
(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
(PARI) isok(k) = fordiv(k, d, if ((d>1) && (d<k) && ((d%10)==1) && (((k/d) % 10) == 1), return (1))); \\ Michel Marcus, Jul 28 2021
CROSSREFS
Cf. A017281 (supersequence), A053742 (ending with 5), A324297 (ending with 6), A346508, A346509, A346510.
Sequence in context: A037050 A275028 A036309 * A119378 A261618 A084998
KEYWORD
nonn,base
AUTHOR
Stefano Spezia, Jul 21 2021
STATUS
approved