A329425 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.

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

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.

Eric Angelini, Prime sums from neighbouring terms [Cached copy of html file, with permission]

Eric Angelini, Prime sums from neighbouring terms [Cached copy of pdf file, with permission]

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

Cf. A055265, A128280 (1 prime from 2 terms), A329333 (1 prime from 3 terms), A329405-A329416 (N primes from M terms >= 1), A329449, ..., A329581 (N primes from M terms >= 0).

Sequence in context: A210747 A353239 A351497 * A379263 A373390 A247942

Adjacent sequences: A329422 A329423 A329424 * A329426 A329427 A329428

Keyword

nonn

Author

M. F. Hasler, following an idea from Eric Angelini, Nov 24 2019

Status

approved