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A075712
Rearrangement of primes into Germain groups (or Cunningham chains).
7
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
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
See also A181697.
See A059456 for initial terms, A338945 for lengths.
Sequence in context: A248646 A093053 A192580 * A349411 A347309 A174162
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