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

Author

M. F. Hasler, Feb 09 2020

Keywords

• nonn

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.

Examples

			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.
		

Links

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

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.

Programs

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