A189788 Base-10 lunar factorials: a(n) = (lunar) Product_{i=1..n} i.

9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 110, 1110, 11110, 111110, 1111110, 11111110, 111111110, 1111111110, 11111111110, 111111111100, 1111111111100, 11111111111100, 111111111111100, 1111111111111100, 11111111111111100, 111111111111111100, 1111111111111111100, 11111111111111111100, 111111111111111111100, 1111111111111111111000

Offset

0,1

Comments

0!, the empty product, equals 9 (the multiplicative identity) by convention.

Links

M. F. Hasler, Table of n, a(n) for n = 0..200

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arXiv:1107.1130 [math.NT], 2011. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.

Index entries for sequences related to dismal (or lunar) arithmetic

Example

4! = 1 X 2 X 3 X 4 = 1, where X is lunar multiplication, A087062.

Prog

(PARI) apply( A189788(n)=if(n>9, for(k=10, n-1, n=A087062(n, k)); n, 9^!n), [0..30]) \\ M. F. Hasler, Nov 15 2018
(Python) # uses lunar_mul and lunar_add from A087062
from functools import reduce
def a(n): return reduce(lunar_mul, [9]+list(range(1, n+1)))
print([a(n) for n in range(31)]) # Michael S. Branicky, Sep 01 2021
(Python) # uses lunar_mul and lunar_add from A087062
from itertools import accumulate
def aupton(nn): return list(accumulate([9]+list(range(1, nn+1)), lunar_mul))
print(aupton(30)) # Michael S. Branicky, Sep 01 2021

Crossrefs

Cf. A087062 (lunar product), A087019 (lunar squares).

Sequence in context: A266557 A010534 A078297 * A264981 A370240 A113061

Adjacent sequences: A189785 A189786 A189787 * A189789 A189790 A189791

Keyword

nonn,base

Author

N. J. A. Sloane, May 23 2011

Extensions

a(0) = 9 prepended and minor edits by M. F. Hasler, Nov 15 2018

Status

approved