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

1,1

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.

Links

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

Example

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.

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]

Crossrefs

Cf. A132199, A137613, A221869.

Sequence in context: A168323 A154561 A073653 * A145398 A087322 A094747

Adjacent sequences: A225484 A225485 A225486 * A225488 A225489 A225490

Keyword

nonn

Author

Jonathan Sondow, May 08 2013

Extensions

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

Status

approved