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a(1) = 1; thereafter, a(n) is the reversal of the next prime after a(n - 1) in base 3 if n is prime, and the reversal of the next composite after a(n - 1) in base 3 if n is composite.
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%I #30 Sep 14 2019 17:51:56

%S 1,2,1,4,7,8,19,20,5,2,1,4,7,8,1,4,7,8,19,20,5,2,1,4,2,4,2,4,7,8,19,

%T 20,5,2,4,2,1,4,2,4,7,8,19,20,5,2,1,4,2,4,2,4,7,8,1,4,2,4,7,8,19,20,5,

%U 2,4,2,1,4,2,4,7,8,19,20,5,2,4,2,1,4,2,4,7,8,1,4,2,4,7,8,1,4,2

%N a(1) = 1; thereafter, a(n) is the reversal of the next prime after a(n - 1) in base 3 if n is prime, and the reversal of the next composite after a(n - 1) in base 3 if n is composite.

%C The sequence is written in base 10.

%C _Rémy Sigrist_'s argument from A326344 gives an upper bound of 23, although the true maximum value is 20, as confirmed by _Andrew Weimholt_'s argument from A326344.

%H N. J. A. Sloane, <a href="/A326894/b326894.txt">Table of n, a(n) for n = 1..20000</a>

%H Robert Dougherty-Bliss, <a href="/A326894/a326894.txt">Proof that A326894 is bounded with maximum value 20</a>

%e By definition, a(1) = 1. The next composite after a(3) = 1 is 4, or 11 in base 3. Reversed this is still 11 in base 3, or 4 in base 10. Thus a(4) = 4 since 4 is composite.

%Y Cf. A326344, A326892, A151800, A113646.

%K nonn,base

%O 1,2

%A _Robert Dougherty-Bliss_, Sep 13 2019

%E Corrected by _N. J. A. Sloane_, Sep 13 2019