OFFSET
0,3
COMMENTS
That is, there are 12 primes, counted with multiplicity, among the 21 pairwise sums of any 7 consecutive terms.
This is the theoretical maximum: there can't be more than 12 primes in pairwise sums of 7 distinct numbers > 1. See the wiki page for more details.
Conjectured to be a permutation of the nonnegative integers. See A329573 for the "positive" variant: same definition but with offset 1 and positive terms, leading to a quite different sequence.
For a(3) and a(4) resp. a(5) one must forbid the values < 5 resp. < 11 which would be the greedy choices, in order to get a solution for a(7), but from then on, the greedy choice gives the correct solution, at least for several hundred terms.
LINKS
M. F. Hasler, Prime sums from neighboring terms, OEIS wiki, Nov. 23, 2019
PROG
(PARI) {A329572(n, show=0, o=0, N=12, M=6, D=[3, 5, 4, 6, 5, 11], p=[], u=o, U)=for(n=o+1, n, show>0&& print1(o", "); show<0&& listput(L, o); U+=1<<(o-u); U>>=-u+u+=valuation(U+1, 2); p=concat(if(#p>=M, p[^1], p), o); D&& D[1]==n&& [o=D[2], D=D[3..-1]]&& next; my(c=N-sum(i=2, #p, sum(j=1, i-1, isprime(p[i]+p[j])))); for(k=u, oo, bittest(U, k-u)|| min(c-#[0|p<-p, isprime(p+k)], #p>=M)|| [o=k, break])); show&&print([u]); o} \\ optional args: show=1: print a(o..n-1), show=-1: append them on global list L, in both cases print [least unused number] at the end. See the wiki page for more.
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved