A328720 The position function the fractalization of which yields A328719.

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

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: A057567 A353845 A217895 * A005128 A187782 A129296

Adjacent sequences: A328717 A328718 A328719 * A328721 A328722 A328723

Keyword

nonn

Author

Luc Rousseau, Oct 26 2019

Status

approved