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A318351 a(n) is the smallest prime p such that the sum of the first 2*n + 1 odd primes starting with p is prime. 1
3, 5, 5, 17, 3, 5, 29, 3, 3, 11, 7, 7, 5, 7, 13, 13, 7, 5, 5, 13, 7, 7, 7, 7, 11, 17, 3, 3, 97, 29, 3, 13, 3, 19, 19, 3, 5, 3, 23, 7, 11, 53, 31, 89, 53, 19, 11, 3, 17, 23, 83, 11, 5, 47, 37, 5, 17, 3, 3, 29, 23, 5, 5, 5, 59, 7, 7, 31, 3, 67, 3, 3, 89, 71, 31, 41, 29 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Conjecture: Sequence is bounded.

The sum of consecutive odd primes is the difference of two terms of A007504, which might be used to find terms for this sequence. - David A. Corneth, Aug 25 2018

Apart from the first term the same as A089793. - R. J. Mathar, Nov 02 2018

LINKS

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

EXAMPLE

a(1) = 5 because 3 + 5 + 7 = 15 but 5 + 7 + 11 = 23.

From David A. Corneth, Sep 04 2018: (Start)

Partial sums of the primes is sequence A007504; 2, 5, 10, 17, 28, 41, 58, 77, 100, 129, 160, 197, ...

For n = 1, the least k such that A007504(k + 2*n + 1) - A007504(k) is prime is at k = 2 so a(1) is prime(k + 1) = prime(3) = 5.

(End)

MAPLE

N:= 100: # to get a(0)..a(N)

Primes:= [0, seq(ithprime(i), i=2..5/2*N)]:

PS:= ListTools:-PartialSums(Primes):

found:= true:

for n from 0 to 100 while found do

  found:= false;

  for k from 1 to 5/2*N - (2*n+1) do

    if isprime(PS[k+2*n+1]-PS[k]) then

      found:= true; A[n]:= Primes[k+1]; break

    fi

  od

od:

seq(A[n], n=0..N); # Robert Israel, Oct 21 2018

MATHEMATICA

Array[Block[{k = 1}, While[! PrimeQ@ Total@ Prime[k + Range[2 # + 1]], k++]; Prime[k + 1]] &, 77, 0] (* Michael De Vlieger, Aug 25 2018 *)

PROG

(PARI) a(n) = {c = 2*n + 1; t=2; while(!isprime(sum(i = t, t + c - 1, prime(i))), t++); prime(t)} \\ David A. Corneth, Sep 04 2018

(PARI) upto(n) = {c = n<<1; c += (1-c%2); my(primeSums = List([3]), res = List([3])); t=0; forprime(p = 3, prime(c), t++; listput(primeSums, primeSums[t] + p)); forstep(i = 3, #primeSums, 2, for(j = 1, #primeSums - i,   if(isprime(primeSums[i + j] - primeSums[j]), listput(res,  primeSums[j+1] - primeSums[j]); next(2)))); res} \\ gives at most the first n terms \\ David A. Corneth, Sep 04 2018

CROSSREFS

Cf. A000040, A007504, A065091, A071148.

Sequence in context: A028265 A084041 A028254 * A137780 A079372 A055382

Adjacent sequences:  A318348 A318349 A318350 * A318352 A318353 A318354

KEYWORD

nonn

AUTHOR

David James Sycamore, Aug 24 2018

STATUS

approved

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Last modified November 28 12:22 EST 2021. Contains 349401 sequences. (Running on oeis4.)