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A329406
Lexicographically earliest sequence of distinct positive numbers such that among the pairwise sums of any four consecutive terms there is exactly one prime sum.
12
1, 2, 7, 8, 4, 14, 11, 5, 10, 3, 15, 6, 13, 9, 12, 16, 17, 18, 19, 21, 27, 24, 22, 20, 25, 26, 23, 28, 30, 32, 33, 31, 29, 34, 36, 35, 40, 41, 39, 37, 38, 42, 43, 45, 44, 47, 46, 50, 48, 49, 56, 62, 52, 53, 54, 58, 57, 51, 59, 68, 55, 60, 63, 64, 61, 65, 67, 74, 69, 72, 70, 66, 71, 75, 77, 76, 78
OFFSET
1,2
COMMENTS
For all n >= 1, there is exactly one prime in {a(n+i) + a(n+j), 0 <= i < j <= 3}. See A329450, A329452 onwards for variants for nonnegative integers. - M. F. Hasler, Nov 14 2019
LINKS
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 one prime sum too many.
a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce one prime sum too many.
a(5) = 4 as a(5) = 3 would produce two primes instead of one (3 + 2 = 5 and 3 + 8 = 11); with a(5) = 4 we have the single prime sum we need among the last 4 integers {2,7,8,4}: 11 = 4 + 7.
And so on.
CROSSREFS
Cf. A329333 (3 consecutive terms, exactly 1 prime sum). See also A329450, A329452 onwards.
Sequence in context: A202355 A202357 A334378 * A360441 A019731 A363438
KEYWORD
nonn
AUTHOR
STATUS
approved