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 A281013 Tetrangle T(n,k,i) = i-th part of k-th prime composition of n. 16
 1, 2, 2, 1, 3, 2, 1, 1, 3, 1, 4, 2, 1, 1, 1, 2, 2, 1, 3, 1, 1, 3, 2, 4, 1, 5, 2, 1, 1, 1, 1, 2, 2, 1, 1, 3, 1, 1, 1, 3, 1, 2, 3, 2, 1, 4, 1, 1, 4, 2, 5, 1, 6, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 3, 1, 1, 1, 1, 3, 1, 1, 2, 3, 1, 2, 1, 3, 2, 1, 1, 3, 2, 2, 3, 3, 1, 4, 1, 1, 1, 4, 1, 2, 4, 2, 1, 4, 3, 5, 1, 1, 5, 2, 6, 1, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The *-product of two or more finite sequences is defined to be the lexicographically minimal sequence obtainable by shuffling them together. Every finite positive integer sequence has a unique *-factorization using prime compositions P = {(1), (2), (21), (3), (211), ...}. See A060223 and A228369 for details. These are co-Lyndon compositions, ordered first by sum and then lexicographically. - Gus Wiseman, Nov 15 2019 LINKS Table of n, a(n) for n=1..116. FORMULA Row lengths are A059966(n) = number of prime compositions of n. EXAMPLE The prime factorization of (1, 1, 4, 2, 3, 1, 5, 5) is: (11423155) = (1)*(1)*(5)*(5)*(4231). The prime factorizations of the initial terms of A000002 are: (1) = (1) (12) = (1)*(2) (122) = (1)*(2)*(2) (1221) = (1)*(221) (12211) = (1)*(2211) (122112) = (1)*(2)*(2211) (1221121) = (1)*(221121) (12211212) = (1)*(2)*(221121) (122112122) = (1)*(2)*(2)*(221121) (1221121221) = (1)*(221)*(221121) (12211212212) = (1)*(2)*(221)*(221121) (122112122122) = (1)*(2)*(2)*(221)*(221121). Read as a sequence: (1), (2), (21), (3), (211), (31), (4), (2111), (221), (311), (32), (41), (5). Read as a triangle: (1) (2) (21), (3) (211), (31), (4) (2111), (221), (311), (32), (41), (5). Read as a sequence of triangles: 1 2 2 1 2 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 1 1 3 3 1 2 2 1 2 2 1 1 2 1 2 1 1 4 3 1 1 3 1 1 1 2 2 1 1 1 3 2 3 1 2 2 2 2 1 4 1 3 2 1 3 1 1 1 1 5 4 1 1 3 1 1 2 4 2 3 1 2 1 5 1 3 2 1 1 6 3 2 2 3 3 1 4 1 1 1 4 1 2 4 2 1 4 3 5 1 1 5 2 6 1 7. MATHEMATICA colynQ[q_]:=Array[Union[{RotateRight[q, #], q}]=={RotateRight[q, #], q}&, Length[q]-1, 1, And]; lexsort[f_, c_]:=OrderedQ[PadRight[{f, c}]]; Table[Sort[Select[Join@@Permutations/@IntegerPartitions[n], colynQ], lexsort], {n, 5}] (* Gus Wiseman, Nov 15 2019 *) CROSSREFS Cf. A000740, A215474, A228369, A277427. The binary version is A329318. The binary non-"co" version is A102659. A sequence listing all Lyndon compositions is A294859. Numbers whose binary expansion is co-Lyndon are A328596. Numbers whose binary expansion is co-Lyndon are A275692. Binary Lyndon words are A001037. Lyndon compositions are A059966. Normal Lyndon words are A060223. Cf. A211097, A211100, A296372, A296373, A298941, A329131, A329312, A329313, A329314, A329324, A329326. Sequence in context: A182490 A053274 A243926 * A190683 A181810 A339304 Adjacent sequences: A281010 A281011 A281012 * A281014 A281015 A281016 KEYWORD nonn,tabf AUTHOR Gus Wiseman, Jan 12 2017 STATUS approved

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