A309275 - OEIS

%I #14 Sep 16 2019 04:44:51

%S 1,3,9,2,5,15,7,4,6,27,11,18,13,21,35,8,12,17,19,10,14,33,23,36,20,25,

%T 39,42,29,45,31,16,22,51,85,30,37,57,117,26,41,63,43,66,54,69,47,24,

%U 28,49,75,34,53,81,55,44,38,87,59,90,61,93,189,32,40,65,67,102

%N a(n) is the smallest divisor not yet in the sequence of 3*T(n)= 3*n(n-1)/2, where T(n) are the triangular numbers; n => 1.

%C Up to n = 10000, 1160 of the first 1228 odd primes appear as fixed points of a(n).

%H Enrique Navarrete and Daniel Orellana, <a href="http://arxiv.org/abs/1907.10023">Finding Prime Numbers as Fixed Points of Sequences</a>, arXiv:1907.10023 [math.NT], 2019.

%e For n = 7, 3*T(7) = 63, and a(7) = 7 is a fixed point and the smallest divisor of 63 not yet in the sequence.

%e For n = 43, 3*T(43) = 2709, and a(43) = 43 is a fixed point and the smallest divisor of 2709 not yet in the sequence.

%Y Cf. A000217, A111273.

%K nonn

%O 1,2

%A _Enrique Navarrete_, Jul 20 2019