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A329407 Lexicographically earliest sequence of distinct positive numbers such that among the pairwise sums of any five consecutive terms there is exactly one prime sum. 1
1, 2, 7, 8, 13, 12, 14, 4, 20, 21, 6, 18, 15, 10, 3, 17, 5, 11, 16, 25, 9, 19, 23, 30, 26, 32, 22, 33, 24, 27, 28, 36, 29, 34, 35, 40, 31, 41, 37, 44, 38, 43, 39, 42, 45, 46, 47, 48, 49, 68, 51, 57, 54, 53, 61, 58, 62, 50, 52, 59, 56, 60, 55, 67, 63, 65, 66, 69, 75, 77, 64, 71, 70, 72, 73, 76, 74, 80 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 1 by minimality.

a(2) = 2 as 2 is the smallest available integer not leading to a contradiction. Note that as 1 + 2 = 3 we already have our prime sum.

a(3) = 7 as a(3) = 3, 4, 5 or 6 would produce at least one prime sum too many.

a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce at least one prime sum too many.

a(5) = 13 as a(5) = 3, 4, 5, 6, 9, 10, 11 or 12 would also produce at least one prime sum too many.

a(6) = 12 and we have the single prime sum we need among the last 5 integers {2,7,8,13,12}, which is 19 = 12 + 7.

And so on.

CROSSREFS

Cf. A329333 (3 consecutive terms, exactly 1 prime sum). See also A329450, A329452 onwards.

Sequence in context: A070044 A129850 A037073 * A329408 A047239 A329410

Adjacent sequences:  A329404 A329405 A329406 * A329408 A329409 A329410

KEYWORD

nonn,changed

AUTHOR

Eric Angelini and Jean-Marc Falcoz, Nov 13 2019

STATUS

approved

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Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)