%I #11 Sep 15 2016 11:07:35
%S 3,23,53,197,127,233,691,379,499,857,953,1151,1259,1583,2099,2399,
%T 2417,2579,2909,3803,3821,4217,4651,5107,5813,6829,6079,6599,14153,
%U 10091,8273,10163,9521,12281,13043,11597,12713,13099,16763,15527,16823,22741
%N Smallest odd prime that is the sum of 2n+1 consecutive primes.
%F The sum of the reciprocals = 0.4304...
%e For n = 2,
%e 2+3+5+7+11=28
%e 3+5+7+11+13=39
%e 5+7+11+13+17=53
%e so 53 is the first prime that is the sum of 5 consecutive primes
%t 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 *)
%o (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) }
%Y See A070934 for another version.
%Y Cf. A034962, A082246, A082251, A127340, A127341, A161612, A215991-A216020.
%K easy,nonn
%O 0,1
%A _Cino Hilliard_, May 09 2003