cp's OEIS Frontend

A235165 Primes which are sum of the first k consecutive composite numbers and such that the sum of the first consecutive k+1 composites and the sum of the first k+2 consecutive composites are also prime.

%I A235165 #12 Sep 30 2017 17:54:28
%S A235165 997,3889,320375057,423704707,3431156159,11650632419,15909713927,
%T A235165 16906981181,18170097067,19703643541,25534764667,65405464363,
%U A235165 89483860811,96873744973,157599307213,161983109531,250812627893,255555662521,304165468751,506667567067,563313151277,641930941499,719915546257,755132545199,988899991367,1002877111091,1013997492671
%N A235165 Primes which are sum of the first k consecutive composite numbers and such that the sum of the first consecutive k+1 composites and the sum of the first k+2 consecutive composites are also prime.
%H A235165 Harvey P. Dale, <a href="/A235165/b235165.txt">Table of n, a(n) for n = 1..1000</a>
%e A235165 a(1) = 997 is prime and sum of the first 35 composites from 4 to 51.
%e A235165 And 997 + 52 = 1049 is prime and 1049 + 54 = 1103 is prime. But 1103 + 55 is even and thus not prime.
%t A235165 Select[Partition[Accumulate[Select[Range[20*10^6],CompositeQ]],3,1], AllTrue[ #,PrimeQ]&][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 30 2017 *)
%o A235165 (PARI) i=0; b=0; for( a=2, 2*10^6, if( !isprime(a) , i=i+1; b=b+a; if(( isprime(b) & isprime(b+a+1) &isprime(a+2)& isprime(b+2*a+4))||(isprime(b)&isprime(a+1)&isprime(b+a+2)&isprime(a+3)&isprime(b+2*a+6)),print1(b,", "))))
%Y A235165 Cf. A053782, A234847.
%K A235165 nonn
%O A235165 1,1
%A A235165 _Robin Garcia_, Jan 04 2014