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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. 23
2, 5, 11, 23, 47 (list; graph; refs; listen; history; text; internal format)



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


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

Wikipedia, Cunningham chain


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.


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 *)


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

Sequence in context: A140992 A248646 A093053 * A075712 A174162 A340799

Adjacent sequences:  A192577 A192578 A192579 * A192581 A192582 A192583




Clark Kimberling, Jul 04 2011



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Last modified June 23 23:39 EDT 2021. Contains 345403 sequences. (Running on oeis4.)