A288041 Numbers k such that prime(k) + prime(k+1) + ... + prime(k+4) is prime.

3, 4, 5, 6, 8, 10, 11, 14, 16, 17, 19, 21, 22, 28, 29, 30, 31, 33, 35, 36, 37, 38, 41, 43, 47, 48, 50, 56, 57, 63, 64, 70, 71, 72, 75, 76, 79, 80, 81, 84, 86, 87, 89, 91, 92, 98, 99, 100, 102, 104, 105, 106, 109, 112, 114, 119, 123, 125, 134, 140, 141, 142, 146, 148, 149, 150

Offset: 1

Author

Zak Seidov, Jun 04 2017

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720 (PrimePi), A072225 (numbers n such that prime(n) + prime(n+1) + prime(n+2) is prime), A073681 (smallest of three consecutive primes whose sum is a prime), A152468 (smallest of five consecutive primes whose sum is a prime).

Programs

Mathematica

With[{nn = 154}, Function[s, Select[Range[nn - 4], PrimeQ@ Total@ Take[s, {#, # + 4}] &]]@ Prime@ Range@ nn] (* Michael De Vlieger, Jun 06 2017 *)
Position[Total/@Partition[Prime[Range[200]],5,1],?(PrimeQ[#]&)]//Flatten (* _Harvey P. Dale, Sep 09 2024 *)

PARI

list(lim)=my(v=List(),u=primes(5),n=1); forprime(p=13,, if(n++>lim, break); u=concat(u[2..5],p); if(isprime(vecsum(u)), listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Jun 10 2017

Formula

a(n) = pi(A152468(n)) = A000720(A152468(n)).