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

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

Author

Cino Hilliard, May 09 2003

Keywords

• easy
• nonn

Examples

			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
		

Links

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

Crossrefs

See A070934 for another version.

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

Programs

Maple

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

Mathematica

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 *)

PARI

\\ 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) }

Formula

The sum of the reciprocals = 0.4304...