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A075712

Rearrangement of primes into Germain groups (or Cunningham chains).

2, 5, 11, 23, 47, 3, 7, 13, 17, 19, 29, 59, 31, 37, 41, 83, 167, 43, 53, 107, 61, 67, 71, 73, 79, 89, 179, 359, 719, 1439, 2879, 97, 101, 103, 109, 113, 227, 127, 131, 263, 137, 139, 149, 151, 157, 163, 173, 347, 181, 191, 383, 193, 197, 199, 211, 223, 229, 233

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OFFSET

1,1

COMMENTS

In each group, p(i+1) = 2*p(i)+1.

The groups are also known as Cunningham chains of the first kind.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

EXAMPLE

The groups are:

{2, 5, 11, 23, 47},

{3, 7},

{13},

{17},

{19},

{29, 59},

{31},

{37},

{41, 83, 167},

{43},

{53, 107},

{61},

{67},

{71},

{73},

{79},

{89, 179, 359, 719, 1439, 2879},

{97},

{101},

{103},

{109},

{113, 227},

{127},

{131, 263},

{137},

{139},

...

MATHEMATICA

Block[{a = {2}, j = 1, k, p}, Do[k = j; If[PrimeQ@ a[[-1]], AppendTo[a, 2 a[[-1]] + 1], While[! FreeQ[a, Set[p, Prime[k]]], k++]; j++; Set[a, Append[a[[1 ;; -2]], p]]], 10^3]; a] (* Michael De Vlieger, Nov 17 2020 *)

PROG

(PARI) first(n) = my(res=List([2, 5, 11, 23, 47])); forprime(p=3, oo, if(!isprime((p-1)>>1), listput(res, p); c = 2*p+1; while(isprime(c), listput(res, c); c=2*c+1)); if(#res>n, return(res))); res \\ David A. Corneth, Nov 13 2021

CROSSREFS

Cf. A005384, A059452, A059453, A059455, A059456, A053176.

URL: https://oeis.org/A075712

⇱ A075712 - OEIS