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 A334435 Heinz numbers of all reversed integer partitions sorted first by sum, then by length, and finally reverse-lexicographically. 32
 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 12, 16, 11, 15, 14, 18, 20, 24, 32, 13, 25, 21, 22, 27, 30, 28, 36, 40, 48, 64, 17, 35, 33, 26, 45, 50, 42, 44, 54, 60, 56, 72, 80, 96, 128, 19, 49, 55, 39, 34, 75, 63, 70, 66, 52, 81, 90, 100, 84, 88, 108, 120, 112, 144, 160, 192, 256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First differs from A334433 at a(75) = 99, A334433(75) = 98. First differs from A334436 at a(22) = 22, A334436(22) = 27. A permutation of the positive integers. Reversed integer partitions are finite weakly increasing sequences of positive integers. This is the Abramowitz-Stegun ordering of reversed partitions (A185974) except that the finer order is reverse-lexicographic instead of lexicographic. The version for non-reversed partitions is A334438. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions. As a triangle with row lengths A000041, the sequence starts {{1},{2},{3,4},{5,6,8},...}, so offset is 0. LINKS Wikiversity, Lexicographic and colexicographic order FORMULA A001222(a(n)) = A036043(n). EXAMPLE The sequence of terms together with their prime indices begins: 1: {} 32: {1,1,1,1,1} 42: {1,2,4} 2: {1} 13: {6} 44: {1,1,5} 3: {2} 25: {3,3} 54: {1,2,2,2} 4: {1,1} 21: {2,4} 60: {1,1,2,3} 5: {3} 22: {1,5} 56: {1,1,1,4} 6: {1,2} 27: {2,2,2} 72: {1,1,1,2,2} 8: {1,1,1} 30: {1,2,3} 80: {1,1,1,1,3} 7: {4} 28: {1,1,4} 96: {1,1,1,1,1,2} 9: {2,2} 36: {1,1,2,2} 128: {1,1,1,1,1,1,1} 10: {1,3} 40: {1,1,1,3} 19: {8} 12: {1,1,2} 48: {1,1,1,1,2} 49: {4,4} 16: {1,1,1,1} 64: {1,1,1,1,1,1} 55: {3,5} 11: {5} 17: {7} 39: {2,6} 15: {2,3} 35: {3,4} 34: {1,7} 14: {1,4} 33: {2,5} 75: {2,3,3} 18: {1,2,2} 26: {1,6} 63: {2,2,4} 20: {1,1,3} 45: {2,2,3} 70: {1,3,4} 24: {1,1,1,2} 50: {1,3,3} 66: {1,2,5} Triangle begins: 1 2 3 4 5 6 8 7 9 10 12 16 11 15 14 18 20 24 32 13 25 21 22 27 30 28 36 40 48 64 17 35 33 26 45 50 42 44 54 60 56 72 80 96 128 This corresponds to the following tetrangle: 0 (1) (2)(11) (3)(12)(111) (4)(22)(13)(112)(1111) (5)(23)(14)(122)(113)(1112)(11111) MATHEMATICA revlensort[f_, c_]:=If[Length[f]!=Length[c], Length[f]

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Last modified December 7 21:53 EST 2022. Contains 358670 sequences. (Running on oeis4.)