A216020 -id:A216020 - cp's OEIS frontend

A215991 Primes that are the sum of 25 consecutive primes.

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

Offset: 1

Syed Iddi Hasan, Aug 30 2012

nonn

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.

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

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.

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

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

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 *)

psumprm(m, n)={my(list=List(), s=sum(j=1,m,prime(j)), i=1); while(#listAndrew Howroyd, Feb 11 2018

A070934 Smallest prime equal to the sum of 2n+1 consecutive primes.

Original entry on oeis.org

2, 23, 53, 197, 127, 233, 691, 379, 499, 857, 953, 1151, 1259, 1583, 2099, 2399, 2417, 2579, 2909, 3803, 3821, 4217, 4651, 5107, 5813, 6829, 6079, 6599, 14153, 10091, 8273, 10163, 9521, 12281, 13043, 11597, 12713, 13099, 16763, 15527, 16823, 22741

Offset: 0

Lekraj Beedassy, May 21 2002

nonn

			Every term of the increasing sequence of primes 127, 401, 439, 479, 593,... is splittable into a sum of 9 consecutive odd primes and 127 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 is the least one corresponding to n = 4.

T. D. Noe, Table of n, a(n) for n = 0..10000

Cf. Bisection of A070281.
See A082244 for another version.
Cf. A089793, A215235.
Cf. A034962, A082246, A082251, A127340, A127341, A161612, A215991-A216020.

f[n_] := Block[{k = 1, s},While[s = Sum[Prime[i], {i, k, k + 2n}]; !PrimeQ[s], k++ ]; s]; Table[f[n], {n, 0, 41}] (* Ray Chandler, Sep 27 2006 *)

Corrected and extended by Ray G. Opao, Aug 26 2004

Entry revised by Ray Chandler, Sep 27 2006

A082244 Smallest odd prime that is the sum of 2n+1 consecutive primes.

Original entry on oeis.org

3, 23, 53, 197, 127, 233, 691, 379, 499, 857, 953, 1151, 1259, 1583, 2099, 2399, 2417, 2579, 2909, 3803, 3821, 4217, 4651, 5107, 5813, 6829, 6079, 6599, 14153, 10091, 8273, 10163, 9521, 12281, 13043, 11597, 12713, 13099, 16763, 15527, 16823, 22741

Offset: 0

Cino Hilliard, May 09 2003

			For n = 2,
2+3+5+7+11=28
3+5+7+11+13=39
5+7+11+13+17=53
so 53 is the first prime that is the sum of 5 consecutive primes

Robert Israel, Table of n, a(n) for n = 0..10000

See A070934 for another version.

Cf. A034962, A082246, A082251, A127340, A127341, A161612, A215991-A216020.

P:= select(isprime, [seq(i,i=3..3000,2)]):
S:= [0,op(ListTools:-PartialSums(P))]: nS:= nops(S):
R:= NULL:
for n from 1 do
  found:= false;
  for j from 1 to nS - 2*n + 1 while not found do
    v:= S[j+2*n-1]-S[j];
    if isprime(v) then R:= R,v; found:= true fi
  od;
  if not found then break fi;
od:
R; # Robert Israel, Jan 09 2025

Join[{3},Table[SelectFirst[Total/@Partition[Prime[Range[1000]],2n+1,1],PrimeQ],{n,50}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 15 2016 *)

\\ First prime that the sum of an odd number of consecutive primes
psumprm(n) = { sr=0; forstep(i=1,n,2, s=0; for(j=1,i, s+=prime(j); ); for(x=1,n, s = s - prime(x)+ prime(x+i); if(isprime(s),sr+=1.0/s; print1(s" "); break); ); ); print(); print(sr) }

The sum of the reciprocals = 0.4304...

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A215991 Primes that are the sum of 25 consecutive primes.

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A070934 Smallest prime equal to the sum of 2n+1 consecutive primes.

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A082244 Smallest odd prime that is the sum of 2n+1 consecutive primes.

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