A103873 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.

79432, 100888, 114226, 188044, 309091, 311682, 368760, 503386, 672506, 819256, 1036976, 1127567, 1201734, 1278446, 1430321, 1586850, 1611779, 1692295, 1782769, 2176459, 2351364, 2647632, 2750942, 2914915, 3005743, 3091827, 3249605, 3444784, 3754007, 4018023

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A103874, A103875.

Sequence in context: A157661 A159713 A251208 * A252292 A238177 A237172

Adjacent sequences: A103870 A103871 A103872 * A103874 A103875 A103876

Keyword

nonn

Author

Pierre CAMI, Feb 19 2005

Extensions

More terms from Harvey P. Dale, Aug 14 2015

Status

approved