OFFSET
1,1
COMMENTS
Special primes from A059453.
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.
REFERENCES
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 178 (Rev. ed. 1997).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
EXAMPLE
C7 prime chain is generated from prime a(10) = 24176129 with 2p+1 iterations: 24176129, 48352259, 96704519, 193409039, 386818079, 773636159, 1547272319, 3094544639.
MATHEMATICA
Transpose[Select[{#, Length[NestWhileList[2#+1&, #, PrimeQ]]-1}&/@ Prime[Range[PrimePi[24177000]]], #[[2]]>6&]][[1]]
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 21 2001
EXTENSIONS
Corrected and extended by Harvey P. Dale, Jul 10 2002
More terms from Vladimir Joseph Stephan Orlovsky, Jan 17 2009
Corrected by John Cerkan, Nov 30 2016
STATUS
approved