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

Author

N. J. A. Sloane, May 23 2011

Keywords

• nonn
• base

Comments

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

Examples

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

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

Crossrefs

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

Programs

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

Extensions

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