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A215991 Primes that are the sum of 25 consecutive primes.

%I A215991 #27 Mar 04 2023 15:31:31
%S A215991 1259,1361,2027,2267,2633,3137,3389,4057,5153,6257,6553,7013,7451,
%T A215991 7901,9907,10499,10799,10949,11579,12401,14369,15013,15329,17377,
%U A215991 17903,18251,18427,19309,22441,24023,25057,25229,26041,26699,28111,29017,29207,30707,32939,35051,36583
%N A215991 Primes that are the sum of 25 consecutive primes.
%C A215991 Such sequences already existed for all odd numbers <= 15. I chose the particular points (in A215991-A216020) so that by referring to a particular n-th term of one of these sequences, the expected range of the n-th term of an x-prime sum can be calculated for any odd x<100000.
%H A215991 Syed Iddi Hasan, <a href="/A215991/b215991.txt">Table of n, a(n) for n = 1..10000</a>
%p A215991 select(isprime, [seq(add(ithprime(i+k), i=1..25), k=0..250)]); # _Muniru A Asiru_, Feb 11 2018
%t A215991 Select[ListConvolve[Table[1, 25], Prime[Range[500]]], PrimeQ] (* _Jean-François Alcover_, Jul 01 2018, after _Harvey P. Dale_ *)
%t A215991 Select[Total/@Partition[Prime[Range[300]],25,1],PrimeQ] (* _Harvey P. Dale_, Mar 04 2023 *)
%o A215991 (PARI)
%o A215991 psumprm(m, n)={my(list=List(), s=sum(j=1,m,prime(j)), i=1); while(#list<n, s = s-prime(i)+prime(i+m); i++; if(isprime(s), listput(list, s))); Vec(list)}
%o A215991 psumprm(25, 40) \\ _Andrew Howroyd_, Feb 11 2018
%o A215991 (GAP) P:=Filtered([1..10^4],IsPrime);;
%o A215991 Filtered(List([0..250],k->Sum([1..25],i->P[i+k])),IsPrime); # _Muniru A Asiru_, Feb 11 2018
%Y A215991 Cf. A034962, A034965, A082246, A082251, A127340, A127341, A161612, A215992, A215993, A215994, A215995, A215996, A215997, A215998, A215999, A216000, A216001, A216002, A216003, A216004, A216005, A216006, A216007, A216008, A216009, A216010, A216011, A216012, A216013, A216014, A216015, A216016, A216017, A216018, A216019, A216020.
%K A215991 nonn
%O A215991 1,1
%A A215991 _Syed Iddi Hasan_, Aug 30 2012