This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A288041 #18 Sep 09 2024 19:33:08
%S A288041 3,4,5,6,8,10,11,14,16,17,19,21,22,28,29,30,31,33,35,36,37,38,41,43,
%T A288041 47,48,50,56,57,63,64,70,71,72,75,76,79,80,81,84,86,87,89,91,92,98,99,
%U A288041 100,102,104,105,106,109,112,114,119,123,125,134,140,141,142,146,148,149,150
%N A288041 Numbers k such that prime(k) + prime(k+1) + ... + prime(k+4) is prime.
%H A288041 Charles R Greathouse IV, <a href="/A288041/b288041.txt">Table of n, a(n) for n = 1..10000</a>
%F A288041 a(n) = pi(A152468(n)) = A000720(A152468(n)).
%t A288041 With[{nn = 154}, Function[s, Select[Range[nn - 4], PrimeQ@ Total@ Take[s, {#, # + 4}] &]]@ Prime@ Range@ nn] (* _Michael De Vlieger_, Jun 06 2017 *)
%t A288041 Position[Total/@Partition[Prime[Range[200]],5,1],_?(PrimeQ[#]&)]//Flatten (* _Harvey P. Dale_, Sep 09 2024 *)
%o A288041 (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
%Y A288041 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).
%K A288041 nonn
%O A288041 1,1
%A A288041 _Zak Seidov_, Jun 04 2017