

A221869


New primes found by Rowland's recurrence in the order of their appearance.


4



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

1,1


COMMENTS

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


LINKS



FORMULA

Entries stem from new adjacent differences b(n) = b(n  1) + GCD(n, b(n  1)) where b(1)=7.


EXAMPLE

b(5)b(4) = 1510 = 5, so a(1)=5.
b(6)b(5) = 1815 = 3, so a(2)=3.
b(11)b(10) = 3322 =11, so a(3)=11.


MATHEMATICA

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 *)


PROG

See the Shallit link for code in Haskell and C.
(Haskell)
import Data.Set (singleton, member, insert)
a221869 n = a221869_list !! (n1)
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


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



