A087097 -id:A087097 - cp's OEIS frontend

A084666 Lunar primes that are also rational primes.

19, 29, 59, 79, 89, 97, 109, 409, 419, 439, 509, 619, 659, 709, 719, 739, 769, 809, 829, 839, 859, 907, 919, 929, 937, 947, 967, 1009, 1019, 1039, 1049, 1069, 1091, 1093, 1097, 1109, 1409, 1609, 1709, 1901, 1907, 2029, 2039, 2069, 2089, 2099, 2129, 2179, 2309

Offset: 1

N. J. A. Sloane, Nov 08 2003

nonn

D. Applegate, C program for lunar arithmetic and number theory [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 [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

Intersection of A000040 and A087097.

A088475 Numbers n such that the lunar sum of the distinct lunar prime divisors of n is >= n.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75

Offset: 1

David Applegate, Nov 11 2003

			The only lunar prime that divides 10 is 90: 90*1 = 10 (cf. A087061, A087062, A087097) and 90 >= 10, so 10 is a member. - _N. J. A. Sloane_, Mar 04 2007, corrected Oct 07 2010.

D. Applegate, C program for lunar arithmetic and number theory [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 [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.
Tanya Khovanova, Non Recursions
Index entries for sequences related to dismal (or lunar) arithmetic

Complement is A088472, which starts 1, 2, 3, 4, 5, 6, 7, 8, 9, 100, 110, 112, ...

Definition made more precise by Marc LeBrun, Mar 04 2007

A088479 Numbers n such that the lunar product of the distinct lunar prime divisors of n is equal to n.

Original entry on oeis.org

9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 109, 129, 139, 149, 159, 169, 179, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 209, 219, 239, 249, 259, 269, 279, 289, 290, 291, 292, 293, 294, 295, 296, 297

Offset: 1

David Applegate, Nov 11 2003

nonn

Includes the unit 9, the primes A087097, products of two distinct primes, etc. - N. J. A. Sloane, May 28 2011.

D. Applegate, C program for lunar arithmetic and number theory [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 [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 [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. A087097.

A109752 Using the lunar product (see A087062 for definition), numbers n such that if n divides a*b, then n must divide either a or b. The multiplicative identity, 9, is excluded by convention.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 90

Offset: 1

David Wasserman, Aug 11 2005

This condition is one of the definitions of a prime, so these numbers could be called lunar primes (cf. A087097).

			90 is a member because the lunar multiples of 90 are the same as the numbers ending with a 0 and if neither a nor b ends in 0, then neither does a*b.

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. A087062, A087097.

A151360 Lunar sum of n-th lunar prime and 9.

Original entry on oeis.org

19, 29, 39, 49, 59, 69, 79, 89, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 109, 209, 219, 309, 319, 329, 409, 419, 429, 439, 509, 519, 529, 539, 549, 609, 619, 629, 639, 649, 659, 709, 719, 729, 739, 749, 759, 769, 809, 819, 829, 839, 849, 859, 869, 879, 909, 909, 909, 909, 909, 909, 909, 909, 909, 919, 919, 919, 919, 919, 919, 919, 919, 929, 929, 929, 929, 929, 929, 929, 939, 939, 939, 939, 939, 939, 949, 949, 949, 949, 949, 959, 959, 959, 959, 969, 969, 969, 979, 979, 989

Offset: 1

N. J. A. Sloane, Aug 28 2010

This is the lunar equivalent of A008864 (primes + 1).

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. A087097.

A171816 Smallest number of rank n in the poset of lunar numbers.

Original entry on oeis.org

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

Offset: 0

David Applegate, Marc LeBrun and N. J. A. Sloane, Oct 15 2010

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

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arxiv:1107.1130 (2011).
Index entries for sequences related to dismal (or lunar) arithmetic

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.

Edited by M. F. Hasler, Nov 12 2017

A235641 Number of n-digit lunar primes obtained by promoting the binary templates.

Original entry on oeis.org

0, 18, 81, 1539, 17661, 135489

Offset: 1

Arkadiusz Wesolowski, Apr 20 2014

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], see column (c) of Table 2, p. 10.
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A087062, A087097, A087636.

cp's OEIS Frontend

A084666 Lunar primes that are also rational primes.

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A088475 Numbers n such that the lunar sum of the distinct lunar prime divisors of n is >= n.

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A088479 Numbers n such that the lunar product of the distinct lunar prime divisors of n is equal to n.

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A109752 Using the lunar product (see A087062 for definition), numbers n such that if n divides a*b, then n must divide either a or b. The multiplicative identity, 9, is excluded by convention.

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Examples

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A151360 Lunar sum of n-th lunar prime and 9.

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A171816 Smallest number of rank n in the poset of lunar numbers.

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Comments

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Crossrefs

Extensions

A235641 Number of n-digit lunar primes obtained by promoting the binary templates.

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Keywords

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Crossrefs