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%I #27 Mar 04 2023 15:31:31
%S 1259,1361,2027,2267,2633,3137,3389,4057,5153,6257,6553,7013,7451,
%T 7901,9907,10499,10799,10949,11579,12401,14369,15013,15329,17377,
%U 17903,18251,18427,19309,22441,24023,25057,25229,26041,26699,28111,29017,29207,30707,32939,35051,36583
%N Primes that are the sum of 25 consecutive primes.
%C 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 Syed Iddi Hasan, <a href="/A215991/b215991.txt">Table of n, a(n) for n = 1..10000</a>
%p select(isprime, [seq(add(ithprime(i+k), i=1..25), k=0..250)]); # _Muniru A Asiru_, Feb 11 2018
%t Select[ListConvolve[Table[1, 25], Prime[Range[500]]], PrimeQ] (* _Jean-François Alcover_, Jul 01 2018, after _Harvey P. Dale_ *)
%t Select[Total/@Partition[Prime[Range[300]],25,1],PrimeQ] (* _Harvey P. Dale_, Mar 04 2023 *)
%o (PARI)
%o 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 psumprm(25, 40) \\ _Andrew Howroyd_, Feb 11 2018
%o (GAP) P:=Filtered([1..10^4],IsPrime);;
%o Filtered(List([0..250],k->Sum([1..25],i->P[i+k])),IsPrime); # _Muniru A Asiru_, Feb 11 2018
%Y 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 nonn
%O 1,1
%A _Syed Iddi Hasan_, Aug 30 2012
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