A377469 a(n) = (A003309(n)-1)*a(n-1) (n > 1), a(1) = 1, where A003309 are the ludic numbers.

1, 1, 2, 8, 48, 480, 5760, 92160, 2027520, 48660480, 1362493440, 49049763840, 1961990553600, 82403603251200, 3790565749555200, 197109418976870400, 11826565138612224000, 780553299148406784000, 54638730940388474880000, 4152543551469524090880000, 340508571220500975452160000

Offset

1,3

Comments

The analog of A005867 for ludic numbers A003309 instead of primes A000040. Since A003309(9) = 23 > A000040(8) = 19 is the first term that differs in the two sequences (up to offset and initial 1's), this sequence differs from A005867 also from the 9th term on, which is a(9) = (23-1)*92160 = 2027520 instead of A005867(8) = (19-1)*92160 = 1658880.

This sequence gives the (pseudo) period lengths of the rows of the ludic sieve array A255127, in which row r is pseudo-periodic, A255127(r, c) = A255127(r, c-a(r)) + S(r), with the shift S(r) given by the ludic factorials A376237.

Links

Table of n, a(n) for n=1..21.

Formula

a(n) = A005867(n-1) up to n = 8.

Example

Since A003309 = (1, 2, 3, 5, 7, 11, 13,17, 23, 25, ...), we get:
a(2) = (2-1)*1 = 1, a(3) = (3-1)*1 = 2, a(4) = (5-1)*2 = 8, a(5) = (7-1)*8 = 48,
a(6) = (11-1)*48 = 480, a(7) = (13-1)*480 = 5760, a(8) = (17-1)*2 = 92160,
a(9) = (23-1)*92160 = 2027520, a(10) = (25-1)*2027520 = 48660480, and so on.

Prog

(PARI) apply( {A377469(n) = if(n>1, (A003309(n)-1)*A377469(n-1), 1)}, [1..19])

Crossrefs

Cf. A003309 (ludic numbers), A255127 (ludic sieve array), A376237 (ludic factorials), A005867 (analog of this sequence for primes), A000040 (the primes).

Sequence in context: A185135 A238805 A005867 * A280133 A192411 A179563

Adjacent sequences: A377466 A377467 A377468 * A377470 A377471 A377472

Keyword

nonn

Author

M. F. Hasler, Nov 13 2024

Status

approved