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A075712
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Rearrangement of primes into Germain groups (or Cunningham chains).
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7
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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
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1,1
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COMMENTS
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In each group, p(i+1) = 2*p(i)+1.
The groups are also known as Cunningham chains of the first kind.
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LINKS
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EXAMPLE
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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},
...
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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