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A329425
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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.
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18
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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
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0,3
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COMMENTS
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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.
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LINKS
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MAPLE
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R:= 0, 1, 2, 3, 4:
S:= {R}:
for i from 1 to 100 do
for x from 5 do
if member(x, S) then next fi;
n1:= nops(select(isprime, [seq(seq(R[i+j]+R[i+k], j=1..k-1), k=1..4)]));
if nops(select(isprime, [seq(R[i+j]+x, j=1..4)]))+n1 = 6 then
R:= R, x; S:= S union {x}; break
fi
od od:
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PROG
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(PARI) A329425_upto(N) = S(N, 6, 5, 0) \\ see the wiki page for the function S().
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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