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

3, 5, 11, 7, 13, 101, 47, 53, 23, 19, 29, 37, 31, 41, 83, 73, 17, 43, 67, 157, 179, 167, 79, 443, 139, 113, 137, 97, 233, 61, 823, 71, 103, 151, 199, 499, 181, 229, 353, 313, 1889, 271, 317, 197, 613, 607, 127, 257, 89, 367, 223, 433, 239, 911, 109, 107, 557

Offset: 1

Author

Jonathan Sondow, May 08 2013

Keywords

• nonn

Comments

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).

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

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

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..351

Crossrefs

Cf. A132199, A137613, A221869.

Programs

Mathematica

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]

Extensions

a(12)-a(57) from Giovanni Resta, Apr 08 2016