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A059767 Initial (unsafe) primes of Cunningham chains of first type with length exactly 7.

%I A059767 #30 Jul 15 2024 10:23:19
%S A059767 1122659,2164229,2329469,10257809,10309889,12314699,14030309,14145539,
%T A059767 23103659,24176129,28843649,37088729,42389519,49160099,50785439,
%U A059767 62800169,68718059,88174049,95831189,105388169,121255889,138140729,155439419,159938459,173285999
%N A059767 Initial (unsafe) primes of Cunningham chains of first type with length exactly 7.
%C A059767 Special primes from A059453.
%C A059767 Primes p such that (2^k)*p+(2^k)-1 is also prime for k = 0, 1, 2, 3, 4, 5, 6 and is composite for k = -1 and k = 7.
%D A059767 David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 178 (Rev. ed. 1997).
%H A059767 Amiram Eldar, <a href="/A059767/b059767.txt">Table of n, a(n) for n = 1..1000</a>
%e A059767 C7 prime chain is generated from prime a(10) = 24176129 with 2p+1 iterations: 24176129, 48352259, 96704519, 193409039, 386818079, 773636159, 1547272319, 3094544639.
%t A059767 Transpose[Select[{#, Length[NestWhileList[2#+1&, #, PrimeQ]]-1}&/@ Prime[Range[PrimePi[24177000]]], #[[2]]>6&]][[1]]
%t A059767 Select[Prime[Range[10^6]], PrimeQ[a1=2*#+1]&&PrimeQ[a2=2*a1+1]&&PrimeQ[a3=2*a2+1]&&PrimeQ[a4=2*a3+1]&&PrimeQ[a5=2*a4+1]&&PrimeQ[a6=2*a5+1] &] (* _Vladimir Joseph Stephan Orlovsky_, May 01 2008 *)
%o A059767 (PARI) is(n)=n%30==29 && isprime(n) && isprime(2*n+1) && isprime(4*n+3) && isprime(8*n+7) && isprime(16*n+15) && isprime(32*n+31) && isprime(64*n+63) && !isprime(n\2) && !isprime(128*n+127) \\ _Charles R Greathouse IV_, Dec 01 2016
%Y A059767 Cf. A005384, A005385, A005602, A007700, A023272, A023302, A023330, A059452, A059453, A059454, A059455.
%K A059767 nonn
%O A059767 1,1
%A A059767 _Labos Elemer_, Feb 21 2001
%E A059767 Corrected and extended by _Harvey P. Dale_, Jul 10 2002
%E A059767 More terms from _Vladimir Joseph Stephan Orlovsky_, Jan 17 2009
%E A059767 Corrected by _John Cerkan_, Nov 30 2016