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%I #17 Oct 03 2024 07:38:18
%S 1,2,3,7,15,16,4,8,5,13,29,31,63,64,6,9,18,12,17,19,23,55,72,20,10,21,
%T 32,11,27,36,24,33,14,48,65,22,40,66,25,34,28,35,68,26,37,39,80,38,73,
%U 75,52,67,71,79,95,128,30,96,129,42,69,50,76,49,70,41,43,47,111,144,44,81,46,145,74,53,61,125,130,45,82,132,51,136,54,137,139,143,112
%N a(1) = 1; for n > 1, a(n) is the smallest unused positive number such that (a(n-1) AND a(n)) = a(n-1) if a(n-1) is prime, otherwise (a(n-1) AND a(n)) = 0, where AND is the binary AND operation.
%C The terms form a pattern similar to that in A109812. In the first 250000 terms the fixed points are 1, 2, 3, 8, 3650, 50624, 203074. The sequence is conjectured to be a permutation of the positive integers.
%H Scott R. Shannon, <a href="/A375828/b375828.txt">Table of n, a(n) for n = 1..10000</a>
%H Scott R. Shannon, <a href="/A375828/a375828.png">Image of the first 250000 terms</a>. The green line is a(n) = n.
%e a(5) = 15 as a(4) = 7 = 111_2 is prime, and ((15 = 1111_2) AND 111_2) = 111_2 = 7.
%e a(6) = 16 as a(5) = 15 = 1111_2 is not prime, and ((16 = 10000_2) AND 1111_2) = 0.
%Y Cf. A375829, A109812, A007088, A115510, A000040, A353989.
%K nonn
%O 1,2
%A _Scott R. Shannon_, Aug 30 2024