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A225487 Duplicate primes found by Rowland's recurrence in the order of their reappearance. 2

%I #9 Apr 08 2016 07:34:20

%S 3,5,11,7,13,101,47,53,23,19,29,37,31,41,83,73,17,43,67,157,179,167,

%T 79,443,139,113,137,97,233,61,823,71,103,151,199,499,181,229,353,313,

%U 1889,271,317,197,613,607,127,257,89,367,223,433,239,911,109,107,557

%N Duplicate primes found by Rowland's recurrence in the order of their reappearance.

%C Among the first 10^8 terms of A132199 (Rowland's sequence of 1s and primes), 121 terms are prime. Eleven of them appear more than once, and so are a(1), ..., a(11).

%C Among the first 10^100 terms of A132199 there are 18321 primes; of these, 3074 are distinct and 351 repeated. - _Giovanni Resta_, Apr 08 2016

%C See the crossrefs for references, links, and additional comments.

%H Giovanni Resta, <a href="/A225487/b225487.txt">Table of n, a(n) for n = 1..351</a>

%e The first duplicate in Rowland's sequence of primes A137613 = 5, 3, 11, 3, 23, 3, 47, 3, 5, ... is 3, so a(1) = 3. The second duplicate is 5, so a(2) = 5.

%t t = {}; b1 = 7; Do[b0 = b1; b1 = b0 + GCD[n, b0]; d = b1 - b0; If[d > 1, AppendTo[t, d]], {n, 2, 10^8}]; L = {}; Do[ If[MemberQ[Take[t, n - 1], t[[n]]], AppendTo[L, t[[n]]]], {n, 2, Length[t]}]; DeleteDuplicates[L]

%Y Cf. A132199, A137613, A221869.

%K nonn

%O 1,1

%A _Jonathan Sondow_, May 08 2013

%E a(12)-a(57) from _Giovanni Resta_, Apr 08 2016

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