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A221869
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New primes found by Rowland's recurrence in the order of their appearance.
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4
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5, 3, 11, 23, 47, 101, 7, 13, 233, 467, 941, 1889, 3779, 7559, 15131, 53, 30323, 60647, 121403, 242807, 19, 37, 17, 199, 29, 486041, 421, 972533, 577, 1945649, 163, 3891467, 127, 443, 31, 7783541, 15567089, 5323, 31139561, 41, 62279171, 83, 1103, 124559609
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OFFSET
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1,1
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COMMENTS
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The terms up to 1103 required examining numbers produced by Rowland's recurrence up to n = 10^8. - T. D. Noe, Apr 11 2013
Exactly 177789368686545736460055960459780707068552048703463291 iterations to find the first 1000 terms of this sequence. - T. D. Noe, Apr 13 2013
The first 10^100 terms of Rowland's sequence generate 18321 primes, 3074 of which are distinct. - Giovanni Resta, Apr 08 2016
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LINKS
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FORMULA
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Entries stem from new adjacent differences b(n) = b(n - 1) + GCD(n, b(n - 1)) where b(1)=7.
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EXAMPLE
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b(5)-b(4) = 15-10 = 5, so a(1)=5.
b(6)-b(5) = 18-15 = 3, so a(2)=3.
b(11)-b(10) = 33-22 =11, so a(3)=11.
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MATHEMATICA
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t = {}; b1 = 7; Do[b0 = b1; b1 = b0 + GCD[n, b0]; d = b1 - b0; If[d > 1 && !MemberQ[t, d], AppendTo[t, d]], {n, 2, 10^6}]; t (* T. D. Noe, Apr 10 2013 *)
Rest[ DeleteDuplicates[ f[1] = 7; f[n_] := f[n] = f[n - 1] + GCD[n, f[n - 1]]; Differences[ Table[ f[n], {n, 10^6}]]]] (* Jonathan Sondow, May 03 2013 *)
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PROG
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See the Shallit link for code in Haskell and C.
(Haskell)
import Data.Set (singleton, member, insert)
a221869 n = a221869_list !! (n-1)
a221869_list = f 2 7 (singleton 1) where
f u v s | d `member` s = f (u + 1) (v + d) s
| otherwise = d : f (u + 1) (v + d) (d `insert` s)
where d = gcd u v
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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