

A089793


a(n) = the first prime in the earliest chain of 2n+1 consecutive primes whose sum is prime.


4



2, 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
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OFFSET

0,1


COMMENTS

In general (except possibly when it begins with 2), the sum of an even number of consecutive primes is even  hence the restriction to odd chain lengths.


LINKS

T. D. Noe, Table of n, a(n) for n = 0..10000


EXAMPLE

17 is the first prime in the chain 17, 19, 23, 29, 31, 37, 41, which is the earliest chain of 2 * 3 + 1 = 7 consecutive primes whose sum, 197, is prime. Hence a(3) = 17.


MAPLE

P:=proc(q) local j, k, n; for j from 1 by 2 to q do for n from 1 to q do
if isprime(add(ithprime(k), k=n..n+j1)) then print(ithprime(n));
break; fi; od; od; end: P(10^5); # Paolo P. Lava, May 25 2015


MATHEMATICA

With[{prs=Prime[Range[1000]]}, First[#]&/@Flatten[Table[Select[ Partition[ prs, 2n+1, 1], PrimeQ[Total[#]]&, 1], {n, 0, 80}], 1]] (* Harvey P. Dale, Jun 21 2013 *)


CROSSREFS

Cf. A070934, A215235, A180950, A226380.
Sequence in context: A232316 A184604 A064630 * A076570 A089121 A014442
Adjacent sequences: A089790 A089791 A089792 * A089794 A089795 A089796


KEYWORD

nonn


AUTHOR

Joseph L. Pe, Jan 09 2004


STATUS

approved



