A189788 - OEIS

%I #45 Sep 01 2021 03:59:31

%S 9,1,1,1,1,1,1,1,1,1,10,110,1110,11110,111110,1111110,11111110,

%T 111111110,1111111110,11111111110,111111111100,1111111111100,

%U 11111111111100,111111111111100,1111111111111100,11111111111111100,111111111111111100,1111111111111111100,11111111111111111100,111111111111111111100,1111111111111111111000

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

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

%H M. F. Hasler, <a href="/A189788/b189788.txt">Table of n, a(n) for n = 0..200</a>

%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a>, 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]

%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.html">Dismal Arithmetic</a>, J. Int. Seq. 14 (2011) # 11.9.8.

%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>

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

%o (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

%o (Python) # uses lunar_mul and lunar_add from A087062

%o from functools import reduce

%o def a(n): return reduce(lunar_mul, [9]+list(range(1, n+1)))

%o print([a(n) for n in range(31)]) # _Michael S. Branicky_, Sep 01 2021

%o (Python) # uses lunar_mul and lunar_add from A087062

%o from itertools import accumulate

%o def aupton(nn): return list(accumulate([9]+list(range(1, nn+1)), lunar_mul))

%o print(aupton(30)) # _Michael S. Branicky_, Sep 01 2021

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

%K nonn,base

%O 0,1

%A _N. J. A. Sloane_, May 23 2011

%E a(0) = 9 prepended and minor edits by _M. F. Hasler_, Nov 15 2018