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A190354 Primes p such that p,q,r,s are consecutive primes and 2p+9, 2q+9, 2r+9, 2s+9 are also primes. 1

%I

%S 887,907,4211,6569,8447,23339,23357,30809,33427,33937,38839,57529,

%T 57557,57859,70271,77621,77641,77647,77659,80747,86587,87691,109537,

%U 115769,116041,117251,160681,192781,207797,217387,228257,228281,232457,244339

%N Primes p such that p,q,r,s are consecutive primes and 2p+9, 2q+9, 2r+9, 2s+9 are also primes.

%C The smallest in a group of four consecutive primes in A023207. - _R. J. Mathar_, Jun 02 2011

%H Charles R Greathouse IV, <a href="/A190354/b190354.txt">Table of n, a(n) for n = 1..10000</a>

%p isA023207 := proc(n) isprime(n) and isprime(2*n+9) ; end proc:

%p isA190354 := proc(n) local q,r,s ; if isprime(n) then q := nextprime(n) ; r := nextprime(q) ; s := nextprime(r) ; isA023207(n) and isA023207(q) and isA023207(r) and isA023207(s) ; else return false; end if; end proc:

%p for i from 1 do p := ithprime(i) ; if isA190354(p) then print(p) ; end if; end do: # _R. J. Mathar_, Jun 02 2011

%t p2Q[n_]:=And@@PrimeQ[2#+9&/@n]; Transpose[Select[Partition[Prime[ Range[22000]],4,1],p2Q]][[1]] (* _Harvey P. Dale_, Jun 10 2011 *)

%o (PARI) old(p,k)=while(k--,p=precprime(p-1));p; k=0;forprime(p=2, 1e6,if(isprime(p+p+9),if(k++>3,print1(old(p,4)", ")),k=0))

%K nonn

%O 1,1

%A _Pierre CAMI_, May 09 2011

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Last modified May 24 16:36 EDT 2022. Contains 354042 sequences. (Running on oeis4.)