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A309389 a(n) is the smallest positive divisor not yet in the sequence of 11*A000217(n-1); n >= 1.

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%I A309389 #25 Sep 16 2019 04:45:13
%S A309389 1,11,3,2,5,15,7,4,6,9,55,22,13,77,21,8,17,33,19,10,14,121,23,12,20,
%T A309389 25,27,18,29,87,31,16,24,51,35,30,37,209,39,26,41,123,43,86,45,69,47,
%U A309389 44,28,49,75,34,53,99,135,70,38,57,59,66,61,341,63,32,40,65,67,134,46,105,71,36,73,407,111
%N A309389 a(n) is the smallest positive divisor not yet in the sequence of 11*A000217(n-1); n >= 1.
%C A309389 Up to n=10000, 1176 of the first 1228 odd primes appear as fixed points of a(n), i.e., 95.8%.
%C A309389 Conjecture: for large p prime, the odd primes (except p) appear as fixed points of b(n), where b(n) is the smallest positive divisor not yet in the sequence of p*A000217(n-1); n >= 1 (see link).
%H A309389 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 A309389 For n = 1: a(1) = 1 is the smallest divisor of 11*0 not yet in the sequence.
%e A309389 For n = 23: a(23) = 23 is a fixed point and the smallest divisor of 11*253 not yet in the sequence.
%e A309389 For n = 73: a(73) = 73 is a fixed point and the smallest divisor of 11*2628 not yet in the sequence.
%Y A309389 Cf. A000217, A111273, A309275, A309276, A309387.
%K A309389 nonn
%O A309389 1,2
%A A309389 _Enrique Navarrete_, Jul 27 2019