A329576 For all n >= 1, exactly seven sums are prime among a(n+i) + a(n+j), 0 <= i < j < 6; lexicographically earliest such sequence of distinct positive numbers.

1, 2, 3, 4, 5, 8, 11, 26, 15, 9, 14, 32, 17, 20, 21, 27, 10, 16, 19, 7, 12, 13, 24, 6, 23, 35, 25, 37, 18, 36, 22, 31, 61, 28, 30, 39, 40, 43, 33, 64, 38, 45, 34, 29, 63, 50, 44, 53, 42, 59, 47, 54, 48, 41, 90, 49, 55, 52, 108, 58, 46, 51, 121, 73, 78, 76, 100, 79, 81, 151, 60, 67, 112, 70, 69

Offset

1,2

Comments

That is, there are 7 primes, counted with multiplicity, among the 15 pairwise sums of any 6 consecutive terms.

Conjectured to be a permutation of the positive integers.

Links

Table of n, a(n) for n=1..75.

M. F. Hasler, Prime sums from neighboring terms, OEIS wiki, Nov. 23, 2019

Example

For n = 1, we must forbid the greedy choice for a(6) which would be 6, which leads to a dead end: there is no possibility to find a subsequent term that would give 7 prime sums together with {2, 3, 4, 5, 6}. If we take the next larger possibility, a(6) = 8, then it works for the next and all subsequent terms.

Prog

(PARI) {A329576(n, show=1, o=1, N=7, M=5, X=[[6, 6]], 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); my(c=N-sum(i=2, #p, sum(j=1, i-1, isprime(p[i]+p[j])))); if(#p<M&&sum(i=1, #p, isprime(p[i]+u))<=c, o=u)|| for(k=u, oo, bittest(U, k-u)|| sum(i=1, #p, isprime(p[i]+k))!=c|| setsearch(X, [n, k])|| [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

Cf. A329425 (6 primes using 5 consecutive terms), A329566 (6 primes using 6 consecutive terms).

Cf. A329449 (4 primes using 4 consecutive terms), A329456 (4 primes using 5 consecutive terms).

Cf. A329454 (3 primes using 4 consecutive terms), A329455 (3 primes using 5 consecutive terms).

Cf. A329411 (2 primes using 3 consecutive terms), A329452 (2 primes using 4 consecutive terms), A329453 (2 primes using 5 consecutive terms).

Cf. A329333 (1 (odd) prime using 3 terms), A128280 & A055265 (1 prime using 2 terms); A055266 & A253074 (0 primes using 2 terms), A329405 & A329450 (0 primes using 3 terms), A329406 - A329416, A329563 - A329581: other variants.

Sequence in context: A374782 A210671 A189761 * A101137 A256386 A053021

Adjacent sequences: A329573 A329574 A329575 * A329577 A329578 A329579

Keyword

nonn

Author

M. F. Hasler, Feb 09 2020

Status

approved