A370858 Let L_1 = (1) and L_2 = (1, 2); for any n > 2, L_n is obtained by inserting one n between each pair of consecutive terms of L_{n-1} coprime to n; a(n) gives the number of terms in L_n.

1, 2, 3, 4, 7, 8, 15, 24, 43, 56, 111, 132, 263, 420, 723, 1040, 2079, 2472, 4943, 7448, 13091, 19236, 38471, 45884, 86119, 138024, 248459, 359142, 718283, 764160, 1528319, 2605756, 4858899, 7109964, 13809075, 16009784, 32019567, 52524888, 95697787, 125396930

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Rémy Sigrist, PARI program

Formula

a(p) = 2*a(p-1) - 1 for any odd prime number p.

Example

The first terms, alongside the corresponding lists, are:
  n  a(n)  L n
  -  ----  ---------------------------------------------
  1     1  (1                                          )
  2     2  (1,                                        2)
  3     3  (1,                            3,          2)
  4     4  (1,                4,          3,          2)
  5     7  (1,          5,    4,    5,    3,    5,    2)
  6     8  (1,    6,    5,    4,    5,    3,    5,    2)
  7    15  (1, 7, 6, 7, 5, 7, 4, 7, 5, 7, 3, 7, 5, 7, 2)

Prog

(PARI) See Links section.

Crossrefs

Cf. A370857 (first differences).

Sequence in context: A120611 A092063 A227007 * A126850 A007497 A126882

Adjacent sequences: A370855 A370856 A370857 * A370859 A370860 A370861

Keyword

nonn

Author

Rémy Sigrist, Mar 03 2024

Status

approved