A192580 Monotonic ordering of set S generated by these rules: if x and y are in S and xy+1 is a prime, then xy+1 is in S, and 2 is in S.

2, 5, 11, 23, 47

Offset

1,1

Comments

Following the discussion at A192476, the present sequence introduces a restriction: that the generated terms must be prime. A192580 is the first of an ascending chain of finite sequences, determined by the initial set called "start":

A192580: f(x,y)=xy+1 and start={2}

A192581: f(x,y)=xy+1 and start={2,4}

A192582: f(x,y)=xy+1 and start={2,4,6}

A192583: f(x,y)=xy+1 and start={2,4,6,8}

A192584: f(x,y)=xy+1 and start={2,4,6,8,10}

For other choices of the function f(x,y) and start, see A192585-A192598.

A192580 consists of only 5 terms, A192581 of 7 terms, and A192582 of 28,...; what can be said about the sequence (5,7,28,...)?

2, 5, 11, 23, 47 is the complete Cunningham chain that begins with 2. Each term except the last is a Sophie Germain prime A005384. - Jonathan Sondow, Oct 28 2015

Links

Table of n, a(n) for n=1..5.

Wikipedia, Cunningham chain

Example

2 is in the sequence by decree.
The generated numbers are 5=2*2+1, 11=2*5+1, 23=2*11+1, 47=2*23+1.

Mathematica

start = {2}; primes = Table[Prime[n], {n, 1, 10000}];
f[x_, y_] := If[MemberQ[primes, x*y + 1], x*y + 1]
b[x_] := Block[{w = x}, Select[Union[Flatten[AppendTo[w, Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # < 50000 &]];
t = FixedPoint[b, start]  (* A192580 *)

Crossrefs

Cf. A005384, A192476, A192581, A192582, A192583, A192584.

Sequence in context: A140992 A248646 A093053 * A075712 A349411 A347309

Adjacent sequences: A192577 A192578 A192579 * A192581 A192582 A192583

Keyword

nonn,fini,full

Author

Clark Kimberling, Jul 04 2011

Status

approved