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 A108352 a(n) = primal code characteristic of n, which is the least positive integer, if any, such that (n o)^k = 1, otherwise equal to 0. Here "o" denotes the primal composition operator, as illustrated in A106177 and A108371 and (n o)^k = n o ... o n, with k occurrences of n. 20
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Jon Awbrey, Primal Code Characteristic, n = 1 to 1000 Jon Awbrey, Primal Code Characteristic, n = 1001 to 2000 Jon Awbrey, Primal Code Characteristic, n = 2001 to 3000 EXAMPLE a(1) = 1 because (1 o)^1 = ({ } o)^1 = 1. a(2) = 0 because (2 o)^k = (1:1 o)^k = 2, for all positive k. a(3) = 2 because (3 o)^2 = (2:1 o)^2 = 1. a(4) = 2 because (4 o)^2 = (1:2 o)^2 = 1. a(5) = 2 because (5 o)^2 = (3:1 o)^2 = 1. a(6) = 0 because (6 o)^k = (1:1 2:1 o)^k = 6, for all positive k. a(7) = 2 because (7 o)^2 = (4:1 o)^1 = 1. a(8) = 2 because (8 o)^2 = (1:3 o)^1 = 1. a(9) = 0 because (9 o)^k = (2:2 o)^k = 9, for all positive k. a(10) = 0 because (10 o)^k = (1:1 3:1 o)^k = 10, for all positive k. Detail of calculation for compositional powers of 12: (12 o)^2 = (1:2 2:1) o (1:2 2:1) = (1:1 2:2) = 18 (12 o)^3 = (1:1 2:2) o (1:2 2:1) = (1:2 2:1) = 12 Detail of calculation for compositional powers of 20: (20 o)^2 = (1:2 3:1) o (1:2 3:1) = (3:2) = 25 (20 o)^3 = (3:2) o (1:2 3:1) = 1 CROSSREFS Cf. A055231, A061396, A062504, A062537, A062860, A106177, A106178. Cf. A108353, A108370, A108371, A108372, A108373, A108374, A111801. Sequence in context: A138319 A217864 A002100 * A215883 A036476 A104994 Adjacent sequences:  A108349 A108350 A108351 * A108353 A108354 A108355 KEYWORD nonn AUTHOR Jon Awbrey, May 31 2005, revised Jun 01 2005 EXTENSIONS Links and cross-references added, Aug 19 2005 STATUS approved

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