A216003 -id:A216003

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A215991

Primes that are the sum of 25 consecutive primes.

+10
33

1259, 1361, 2027, 2267, 2633, 3137, 3389, 4057, 5153, 6257, 6553, 7013, 7451, 7901, 9907, 10499, 10799, 10949, 11579, 12401, 14369, 15013, 15329, 17377, 17903, 18251, 18427, 19309, 22441, 24023, 25057, 25229, 26041, 26699, 28111, 29017, 29207, 30707, 32939, 35051, 36583

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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.

LINKS

Syed Iddi Hasan, Table of n, a(n) for n = 1..10000

MAPLE

select(isprime, [seq(add(ithprime(i+k), i=1..25), k=0..250)]); # Muniru A Asiru, Feb 11 2018

MATHEMATICA

Select[ListConvolve[Table[1, 25], Prime[Range[500]]], PrimeQ] (* Jean-François Alcover, Jul 01 2018, after Harvey P. Dale *)

Select[Total/@Partition[Prime[Range[300]], 25, 1], PrimeQ] (* Harvey P. Dale, Mar 04 2023 *)

PROG

(PARI)

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)}

psumprm(25, 40) \\ Andrew Howroyd, Feb 11 2018

(GAP) P:=Filtered([1..10^4], IsPrime);;

Filtered(List([0..250], k->Sum([1..25], i->P[i+k])), IsPrime); # Muniru A Asiru, Feb 11 2018

CROSSREFS

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.

KEYWORD

nonn

AUTHOR

Syed Iddi Hasan, Aug 30 2012

STATUS

approved

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