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
Robert Israel, Table of n, a(n) for n = 0..10000
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.
MAPLE
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:
R; # Robert Israel, Dec 29 2022
PROG
(PARI) A329425_upto(N) = S(N, 6, 5, 0) \\ see the wiki page for the function S().
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, following an idea from Eric Angelini, Nov 24 2019
STATUS
approved