A087019 -id:A087019 - cp's OEIS frontend

A172199 Number of numbers with 2n+1 digits that are lunar squares.

10, 90, 900, 9000, 74667, 608673

Offset: 1

David Applegate, Marc LeBrun and N. J. A. Sloane, Jan 20 2011

Every lunar square (see A087019) has an odd number of digits. Lunar squares with <= 7 digits are all distinct, but for longer numbers there are many examples of pairs of numbers whose lunar squares coincide.

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A087019, A180513, A181319.

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

Original entry on oeis.org

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

N. J. A. Sloane, May 23 2011

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

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

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

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

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

# 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

# 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

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

A171120 Numbers that are the lunar sums of two lunar squares.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 118, 119, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 211, 212, 213, 214, 215, 216, 217, 218, 219, 222, 223, 224, 225, 226

Offset: 1

N. J. A. Sloane, Sep 28 2010

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A087019.

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A172199 Number of numbers with 2n+1 digits that are lunar squares.

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

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A171120 Numbers that are the lunar sums of two lunar squares.

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