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%I #10 Mar 05 2020 21:46:32
%S 79432,100888,114226,188044,309091,311682,368760,503386,672506,819256,
%T 1036976,1127567,1201734,1278446,1430321,1586850,1611779,1692295,
%U 1782769,2176459,2351364,2647632,2750942,2914915,3005743,3091827,3249605,3444784,3754007,4018023
%N Numbers k such that 2*P(k) + 3, 2*P(k+1) + 5, 2*P(k+2) + 7, 2*P(k+3) + 9 are also consecutive primes where P(i) = i-th prime.
%t cpQ[{a_,b_,c_,d_}]:=AllTrue[{2a+3,2b+5,2c+7,2d+9},PrimeQ] && NextPrime[ 2a+3] == 2b+5 && NextPrime[ 2b+5] == 2c+7 && NextPrime[ 2c+7] == 2d+9; PrimePi/@ Transpose[Select[ Partition[Prime[Range[ 1100000]], 4,1], cpQ]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Aug 14 2015 *)
%o (PARI) lista(nn) = {my(k=1, v=[2, 3, 5, 7]); forprime(p=11, nn, k++; v=concat(v[2..4], p); if(ispseudoprime(2*v[1]+3) && nextprime(2*v[1]+4)==2*v[2]+5 && nextprime(2*v[2]+6)==2*v[3]+7 && nextprime(2*v[3]+8)==2*v[4]+9, print1(k, ", "))); } \\ _Jinyuan Wang_, Mar 05 2020
%Y Cf. A103874, A103875.
%K nonn
%O 1,1
%A _Pierre CAMI_, Feb 19 2005
%E More terms from _Harvey P. Dale_, Aug 14 2015
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