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A068066 The sum or half the sum of n consecutive primes starting at a(n) is prime. 0
2, 2, 5, 2, 5, 2, 17, 83, 3, 3, 5, 2, 29, 2, 3, 11, 3, 3, 11, 23, 7, 5, 7, 11, 5, 3, 7, 3, 13, 3, 13, 5, 7, 17, 5, 3, 5, 73, 13, 5, 7, 5, 7, 5, 7, 29, 7, 53, 11, 29, 17, 31, 3, 23, 3, 47, 97, 5, 29, 2, 3, 37, 13, 2, 3, 17, 19, 5, 19, 71, 3, 47, 5, 19, 3, 59, 23, 89, 7, 19, 11, 37, 53, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This eliminates the impossibles out of A007610 and the 'or' in the title is the exclusive or.

LINKS

Table of n, a(n) for n=1..84.

EXAMPLE

a(3) = 5 because 5+7+11 = prime 23 and a(10) = 3 because 3+5+7+11+13+17+19+23+29+31 = 158 and half that or 79 is a prime.

MATHEMATICA

Do[k = n; a = Table[Prime[i], {i, 1, n} ]; While[ !PrimeQ[Plus @@ a] && !PrimeQ[Plus @@ a/2], k++; a = Drop[a, 1]; a = Append[a, Prime[k]]]; Print[a[[1]]], {n, 1, 100} ]

CROSSREFS

Cf. A007610.

Sequence in context: A039931 A128645 A007610 * A171889 A171868 A292146

Adjacent sequences:  A068063 A068064 A068065 * A068067 A068068 A068069

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Feb 16 2002

STATUS

approved

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Last modified February 24 18:55 EST 2021. Contains 341584 sequences. (Running on oeis4.)