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Numbers of rank 2 in the poset of lunar numbers.
+10
7
7, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 108, 119, 129, 139, 149, 159, 169, 179, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 208, 218, 229, 239, 249, 259, 269, 279, 289, 290, 291, 292, 293, 294, 295, 296, 297
LINKS
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]
CROSSREFS
Cf. A087097, A133626, A161813, A144171, A144175, A171786, A171787, A171788, A171789, A171794, A171795, A171796, A191752, A191753.
Rank of n in the lunar poset.
+10
7
8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 8, 8, 8, 7, 6, 5, 4, 3, 2, 1, 7, 7, 7, 7, 6, 5, 4, 3, 2, 1, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1, 5, 5, 5, 5, 5, 5, 4, 3, 2, 1, 4, 4, 4, 4, 4, 4, 4, 3, 2, 1, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 9, 8, 7, 6, 5
LINKS
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]
EXAMPLE
Ranks of the numbers 1 through 99, written in 10 groups of 10 (the dash is for n=0, where the rank is undefined):
- 8 7 6 5 4 3 2 1 0 (1 has rank 8, 2 has rank 7, etc.)
9 9 8 7 6 5 4 3 2 1 (10 has rank 9, 11 has rank 9, etc.)
8 8 8 7 6 5 4 3 2 1
7 7 7 7 6 5 4 3 2 1
6 6 6 6 6 5 4 3 2 1
5 5 5 5 5 5 4 3 2 1
4 4 4 4 4 4 4 3 2 1
3 3 3 3 3 3 3 3 2 1
2 2 2 2 2 2 2 2 2 1
1 1 1 1 1 1 1 1 1 1
CROSSREFS
Cf. A161813, A144171, A144175, A171786, A171787, A171788, A171789, A171794, A171795, A171796, A191752, A191753.
Numbers of rank 9 in the poset of lunar numbers.
+10
7
10, 11, 101, 112, 120, 121, 122, 200, 210, 211, 220, 221, 222, 1001, 1011, 1020, 1101, 1113, 1123, 1130, 1131, 1132, 1133, 1212, 1223, 1230, 1231, 1232, 1233, 1300, 1310, 1311, 1320, 1321, 1322, 1330, 1331, 1332, 1333, 2010, 2020, 2120
LINKS
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]
CROSSREFS
Cf. A161813, A144171, A144175, A171786, A171787, A171788, A171789, A171794, A171795, A171796, A191752, A191753.
Numbers of rank 10 in the poset of lunar numbers.
+10
7
100, 110, 111, 1010, 1112, 1120, 1121, 1122, 1200, 1210, 1211, 1220, 1221, 1222, 2000, 2100, 2110, 2111, 2200, 2210, 2211, 2220, 2221, 2222, 10010, 10101, 10110, 10200, 11010, 11011, 11113, 11123, 11130, 11131, 11132, 11133, 11212, 11223, 11230, 11231, 11232, 11233, 11300, 11310, 11311, 11320, 11321, 11322, 11330, 11331, 11332, 11333, 12120, 12121, 12223, 12230, 12231, 12232
LINKS
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] D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
CROSSREFS
Cf. A161813, A144171, A144175, A171786, A171787, A171788, A171789, A171794, A171795, A171796, A191752, A191753.
Numbers of rank 11 in the poset of lunar numbers.
+10
7
1000, 1100, 1110, 1111, 10100, 11112, 11120, 11121, 11122, 11200, 11210, 11211, 11220, 11221, 11222, 12000, 12100, 12110, 12111, 12200, 12210, 12211, 12220, 12221, 12222, 20000, 21000, 21100, 21110, 21111, 22000, 22100, 22110, 22111, 22200, 22210, 22211, 22220, 22221, 22222
LINKS
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] D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
CROSSREFS
Cf. A161813, A144171, A144175, A171786, A171787, A171788, A171789, A171794, A171795, A171796, A191752, A191753.
Smallest number of rank n in the poset of lunar numbers.
+10
0
9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000, 10000000000000000000
COMMENTS
We have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing. - N. J. A. Sloane, Aug 06 2014
LINKS
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arxiv:1107.1130 (2011).
CROSSREFS
Cf. A087061 (definition of lunar sum and product), A087062 (table of lunar product), A087097 (lunar (formerly dismal) primes). Cf. A161813 (lunar poset rank of n), A144171, A144175, A171786, A171787, A171788, A171789, A171794, A171795, A171796, A191752, A191753.
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