EDITED -- A108352

[Jon Awbrey]

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%I A108352
%S A108352 1,0,2,2,2,0,2,2,0,0,2,0,2,0,2,2,2,0,2,3,
           2,0,2,3,2,0,2,3,2,0,2,2,2,0,2,0,2,0,2,0,
           2,0,2,3,0,0,2,3,2,0,2,3,2,0,2,3,2,0,2,0,
           2,0,2,2,2,0,2,3,2,0,2,0,2,0,3,3,2,0,2,3,
           2,0,2,0,2,0,2,3,2,0,2,3,2,0,2,3,2,0,0,2
%N A108352 a(n) = the primal code characteristic of n,
           which is the least positive integer, if any,
           such that (n o)^k = 1, otherwise equal to 0.
           "o" = primal composition operation, as illustrated in sequence A106177.
           (n o)^k = n o ... o n (with k appearances of n).
%e A108352 Examples:
%e A108352  a(1) = 1 because (1 o)^1 = ({ } o)^1 = 1.
%e A108352  a(2) = 0 because (2 o)^k = (1:1 o)^k = 2, for all positive k.
%e A108352  a(3) = 2 because (3 o)^2 = (2:1 o)^2 = 1.
%e A108352  a(4) = 2 because (4 o)^2 = (1:2 o)^2 = 1.
%e A108352  a(5) = 2 because (5 o)^2 = (3:1 o)^2 = 1.
%e A108352  a(6) = 0 because (6 o)^k = (1:1 2:1 o)^k = 6, for all positive k.
%e A108352  a(7) = 2 because (7 o)^2 = (4:1 o)^1 = 1.
%e A108352  a(8) = 2 because (8 o)^2 = (1:3 o)^1 = 1.
%e A108352  a(9) = 0 because (9 o)^k = (2:2 o)^k = 9, for all positive k.
%e A108352 a(10) = 0 because (10 o)^k = (1:1 3:1 o)^k = 10, for all positive k.
%e A108352 Detail of calculation for compositional powers of 12:
%e A108352 (12 o)^2 = (1:2 2:1) o (1:2 2:1) = (1:1 2:2) = 18
%e A108352 (12 o)^3 = (1:1 2:2) o (1:2 2:1) = (1:2 2:1) = 12
%e A108352 Detail of calculation for compositional powers of 20:
%e A108352 (20 o)^2 = (1:2 3:1) o (1:2 3:1) = (3:2) = 25
%e A108352 (20 o)^3 = (3:2) o (1:2 3:1) = 1
%Y A108352 Cf. A055231, A061396, A062504, A062537, A062860, A106177, A106178.
%K A108352 nonn,new
%O A108352 1,3
%A A108352 Jon Awbrey (jawbrey(AT)att.net), May 31 2005

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