A082244 - OEIS

%I #17 Jan 09 2025 18:56:19

%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.

%H Robert Israel, <a href="/A082244/b082244.txt">Table of n, a(n) for n = 0..10000</a>

%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

%p P:= select(isprime, [seq(i,i=3..3000,2)]):

%p S:= [0,op(ListTools:-PartialSums(P))]: nS:= nops(S):

%p R:= NULL:

%p for n from 1 do

%p   found:= false;

%p   for j from 1 to nS - 2*n + 1 while not found do

%p     v:= S[j+2*n-1]-S[j];

%p     if isprime(v) then R:= R,v; found:= true fi

%p   od;

%p   if not found then break fi;

%p od:

%p R; # _Robert Israel_, Jan 09 2025

%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

%o 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