A087984 9-ish numbers (A011539) which are not lunar primes (A087097).

9, 119, 129, 139, 149, 159, 169, 179, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 229, 239, 249, 259, 269, 279, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 339, 349, 359, 369, 379, 389, 390, 391, 392, 393, 394, 395, 396

Offset: 1

Author

David Applegate and N. J. A. Sloane, Oct 30 2003

Keywords

• nonn
• base

Comments

Three and four digit 9ish numbers are lunar primes iff the smallest digit is strictly smaller than the first and the last digit. This is no longer true from 10109 = 109 x 109 on (where x = lunar product).

Links

• M. F. Hasler, Table of n, a(n) for n = 1..10000
• D. Applegate, C program for lunar arithmetic and number theory
• D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, preprint, arxiv:1107.1130, July 2011. [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.
• Index entries for sequences related to dismal (or lunar) arithmetic

Crossrefs

Cf. A011539, A087097. A133626 and A134211 are subsequences.

Programs

PARI

A087984=setminus(A011539, A087097)
A087984=[9]; for(L=3,4,forvec(d=vector(L,i,[i==1,9]),vecmax(d)==9&&vecmin(d)>=min(d[1],d[L])&&A087984=concat(A087984,fromdigits(d)))) \\ terms with < 5 digits

PARI

is_A087984(n)=vecmax(digits(n))=9&&!is_A087097(n) \\ (End)

Formula

A011539 \ A087097. - M. F. Hasler, Nov 19 2018