

A329425


For all n >= 0, six among (a(n+i) + a(n+j), 0 <= i < j < 5) are prime: lexicographically first such sequence of distinct nonnegative integers.


17



0, 1, 2, 3, 4, 9, 8, 10, 33, 14, 93, 20, 17, 23, 44, 6, 24, 35, 65, 5, 18, 32, 11, 12, 29, 30, 7, 31, 72, 16, 22, 25, 37, 15, 46, 64, 43, 28, 85, 19, 54, 13, 88, 34, 49, 39, 40, 27, 100, 57, 26, 52, 111, 21, 38, 45, 62, 41, 51, 56, 47, 116, 50, 81, 63, 68, 59, 170, 69, 71
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OFFSET

0,3


COMMENTS

The restriction to [1, oo) is the lexicographically first such sequence of positive integers. (This is rather exceptional, cf. A128280 vs A055265, A329405 vs A329450, ..., see the wiki page for more.)
Conjectured to be a permutation, i.e., all n >= 0 appear. The restriction to [1, oo) is then the lexicographically first such permutation of the positive integers.
Among pairwise sums of 5 consecutive terms, there cannot be more than 2 x 3 = 6 primes: see the wiki page for this and further considerations and variants.


LINKS

Table of n, a(n) for n=0..69.
Éric Angelini, Prime sums from neighbouring terms, SeqFan list, and personal blog "Cinquante signes", Nov. 11, 2019.
M. F. Hasler, Prime sums from neighboring terms, OEIS wiki, Nov. 23, 2019.


PROG

(PARI) A329425_upto(N) = S(N, 6, 5, 0) \\ see the wiki page for the function S().


CROSSREFS

Cf. A055265, A128280 (1 prime from 2 terms), A329333 (1 prime from 3 terms), A329405A329416 (N primes from M terms >= 1), A329449, ..., A329581 (N primes from M terms >= 0).
Sequence in context: A307405 A115305 A210747 * A247942 A098550 A256224
Adjacent sequences: A329422 A329423 A329424 * A329426 A329427 A329428


KEYWORD

nonn


AUTHOR

M. F. Hasler, following an idea from Eric Angelini, Nov 24 2019


STATUS

approved



