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

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.

See also A181697.

See A059456 for initial terms, A338945 for lengths.

Sequence in context: A248646 A093053 A192580 * A349411 A347309 A174162

Adjacent sequences: A075709 A075710 A075711 * A075713 A075714 A075715

Keyword

nonn,tabf

Author

Zak Seidov, Oct 03 2002

Extensions

Edited by N. J. A. Sloane, Nov 13 2021

More terms from David A. Corneth, Nov 13 2021

Status

approved