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 A328720 The position function the fractalization of which yields A328719. 1
 1, 2, 2, 4, 2, 5, 2, 8, 5, 7, 2, 11, 2, 9, 7, 16, 2, 14, 2, 17, 9, 13, 2, 23, 9, 15, 14, 23, 2, 22, 2, 32, 13, 19, 11, 32, 2, 21, 15, 37, 2, 30, 2, 35, 22, 25, 2, 47, 14, 34, 19, 41, 2, 41, 17, 51, 21, 31, 2, 52, 2, 33, 30, 64, 19, 46, 2, 53, 25, 46, 2, 68, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For a definition of the fractalization process, see comments in A194959. The sequence A328719, triangular array where row n is the list of the numbers k from 1 to n sorted in ascending lexicographic order of their sequences of p-adic valuations, is clearly the result of a fractalization. Let {a(n)} (this sequence) be its position function. LINKS FORMULA a(1) = 1. a(p) = 2 iff p is a prime number. a(2^k) = 2^k. a(3^k) = (3^k+1)/2 = A007051(k). A328719(n, a(n)) = n. - Rémy Sigrist, Nov 11 2019 EXAMPLE In A328719 in triangular form, rows 19 and 20 are:   1, 19, 17, 13, 11,  7,  5,  3, 15,  9,  2, 14, 10,  6, 18,  4, 12,  8, 16;   1, 19, 17, 13, 11,  7,  5,  3, 15,  9,  2, 14, 10,  6, 18,  4, 20, 12,  8, 16. Row 20 is row 19 in which 20 has been inserted in position 17, so a(20) = 17. PROG (PARI) L=List(); n=1; while(n<=100, i=1; while(i

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Last modified August 13 04:54 EDT 2020. Contains 336442 sequences. (Running on oeis4.)