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A056531 Sequence remaining after a fourth round of Flavius Josephus sieve; remove every fifth term of A056530. 4
1, 3, 7, 13, 19, 25, 27, 31, 39, 43, 49, 51, 61, 63, 67, 73, 79, 85, 87, 91, 99, 103, 109, 111, 121, 123, 127, 133, 139, 145, 147, 151, 159, 163, 169, 171, 181, 183, 187, 193, 199, 205, 207, 211, 219, 223, 229, 231, 241, 243, 247, 253, 259, 265, 267, 271, 279 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Numbers {1, 3, 7, 13, 19, 25, 27, 31, 39, 43, 49, 51} mod 60.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
FORMULA
From Chai Wah Wu, Jul 24 2016: (Start)
a(n) = a(n-1) + a(n-12) - a(n-13) for n > 13.
G.f.: x*(9*x^12 + 2*x^11 + 6*x^10 + 4*x^9 + 8*x^8 + 4*x^7 + 2*x^6 + 6*x^5 + 6*x^4 + 6*x^3 + 4*x^2 + 2*x + 1)/(x^13 - x^12 - x + 1). (End)
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 3, 7, 13, 19, 25, 27, 31, 39, 43, 49, 51, 61}, 60] (* Harvey P. Dale, Mar 11 2019 *)
CROSSREFS
Compare A000027 for 0 rounds of sieve, A005408 after 1 round of sieve, A047241 after 2 rounds, A056530 after 3 rounds, A056531 after 4 rounds, A000960 after all rounds.
After n rounds the remaining sequence comprises A002944(n) numbers mod A003418(n+1), i.e. 1/(n+1) of them.
Sequence in context: A216098 A310262 A310263 * A310264 A144917 A102828
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Jun 19 2000
STATUS
approved

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Last modified April 16 10:37 EDT 2024. Contains 371709 sequences. (Running on oeis4.)