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 A180346 Primes that divide every circular permutation of the digits of at least one number of the form 123...(n-1)(n) (see A007908), where n is 3 digits long (that is, for some n in the range 99
 3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 53, 61, 67, 73, 83, 97, 101, 107, 127, 163, 211, 271, 277, 1009, 18973 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Every a(i) divides at least 192 permutations of the digits of an element belonging to [A007908]. Skipping the trivial case a(1)=3, the most recurring elements are a(2)=7 and a(10)=37. The occurrences in our 1386450 terms set are the following [A181373]: a(2) | 7  ⇒  n=100+14*v       (v=0,1,2,...,64) a(3) | 11 ⇒  n=106+22*v       (v=0,1,2,...,40) a(4) | 13 ⇒  n=120+26*v       (v=0,1,2,...,33) a(5) | 17 ⇒  n=196+272*v      (v=0,1,2) a(6) | 19 ⇒  n=102+114*v      (v=0,1,2,3,4,5,6,7) a(7) | 23 ⇒  n=542 a(8) | 29 ⇒  n=400 a(9) | 31 ⇒  n=181+155*v      (v=0,1,2,3,4,5) a(10)| 37 ⇒  n=123+d(v), (where d(v)=0,12,25,12,25,12,25...  for v=0,1,2,3,...,47) a(11) | 41 ⇒  n=216+205*v     (v=0,1,2,3) a(12) | 43 ⇒  n=372+301*v     (v=0,1,2) a(13) | 53 ⇒  n=127+689*v     (v=0,1) a(14) | 61 ⇒  n=616 a(15) | 67 ⇒  n=399 a(16) | 73 ⇒  n=196+584*v     (v=0,1) a(17) | 83 ⇒  n=118 a(18) | 97 ⇒  n=516 a(19) | 101 ⇒  n=416+404*v    (v=0,1) a(20) | 107 ⇒  n=884 a(21) | 127 ⇒  n=106 a(22) | 163 ⇒  n=576 a(23) | 211 ⇒  n=306 a(24) | 271 ⇒  n=936 a(25) | 277 ⇒  n=174 a(26) | 1009 ⇒ n=960 a(27) | 18973 ⇒ n=903 N.B. Every coefficient of "v" is a multiple of i. This is a general property of [A007908], valid for an arbitrary fixed digits interval of the parameter "n" (10^k-1= prime(10^6) if it exists. - Chai Wah Wu, Nov 12 2015 REFERENCES M. Ripà, "Rudimatematici", Bookshelf, October 2010 Vassilev-Missana and K. Atanassov, “Some Smarandache problems”, Hexis, 2004 LINKS M. Ripà, On prime factors in old and new sequences of integers, vixra.org M. Ripà, Patterns related to the Smarandache circular sequence primality problem, unsolvedproblems.org M. Ripa, Patterns related to the Smarandache circular sequence primality problem, Notes Number Theory Disc. Math 18 (1) (2012) 29-48 F. Smarandache, Only Problems, Not Solutions!, Xiquan Publ., Phoenix-Chicago, 1993. FORMULA For n<10 the only a(i) is 3. If 9

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Last modified April 23 18:06 EDT 2019. Contains 322387 sequences. (Running on oeis4.)