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A075712 Rearrangement of primes into Germain groups. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In each group p(i+1) = 2*p(i)+1: {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}. By the way, it is a question whether the group with one prime is a Germain group. What I call here a Germain group is also known as Cunningham chain of the first kind, A059452, A059453, A059455, A059456, A053176.

LINKS

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

EXAMPLE

First three Germain groups are: {2, 5, 11, 23, 47}, {3, 7}, {13}.

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 *)

CROSSREFS

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

Sequence in context: A248646 A093053 A192580 * A174162 A340799 A186253

Adjacent sequences:  A075709 A075710 A075711 * A075713 A075714 A075715

KEYWORD

nonn,tabf

AUTHOR

Zak Seidov, Oct 03 2002

STATUS

approved

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Last modified June 14 05:51 EDT 2021. Contains 345018 sequences. (Running on oeis4.)