A346507 - OEIS

%I #23 Sep 11 2021 16:06:44

%S 121,231,341,441,451,561,651,671,781,861,891,961,1001,1071,1111,1221,

%T 1271,1281,1331,1441,1491,1551,1581,1661,1681,1701,1771,1881,1891,

%U 1911,1991,2091,2101,2121,2201,2211,2321,2331,2431,2501,2511,2541,2601,2651,2751,2761

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

%C All the terms end with 1 (A017281).

%H Stefano Spezia, <a href="/A346507/b346507.txt">Table of n, a(n) for n = 1..10000</a>

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

%F 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

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

%t 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

%o (Python)

%o 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)))

%o print(aupto(2761)) # _Michael S. Branicky_, Jul 22 2021

%o (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

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

%K nonn,base

%O 1,1

%A _Stefano Spezia_, Jul 21 2021