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

0,1

Links

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

Formula

The sum of the reciprocals = 0.4304...

Example

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

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 *)

Prog

(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) }

Crossrefs

See A070934 for another version.

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

Sequence in context: A032003 A031907 A181422 * A232193 A141047 A196538

Adjacent sequences: A082241 A082242 A082243 * A082245 A082246 A082247

Keyword

easy,nonn

Author

Cino Hilliard, May 09 2003

Status

approved