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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 (list; graph; refs; listen; history; text; internal format)
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+j-1)) 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

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Last modified May 23 12:38 EDT 2019. Contains 323514 sequences. (Running on oeis4.)