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

Author

Zak Seidov, Oct 03 2002

Keywords

• nonn
• tabf

Comments

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

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

Examples

			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},
...
		

Links

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

Crossrefs

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

See also A181697.

See A059456 for initial terms, A338945 for lengths.

Programs

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 *)

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

Extensions

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

More terms from David A. Corneth, Nov 13 2021