

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
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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 padic 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



