

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
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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 += (1c%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



