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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

Table of n, a(n) for n=1..73.

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<n&&factor(L[i]/n)[1, 2]<0, i++); listinsert(L, n, i); print1(i, ", "); n++)

CROSSREFS

Cf. A007051, A194959, A328719.

Sequence in context: A304442 A057567 A217895 * A005128 A187782 A129296

Adjacent sequences:  A328717 A328718 A328719 * A328721 A328722 A328723

KEYWORD

nonn

AUTHOR

Luc Rousseau, Oct 26 2019

STATUS

approved

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