A329577 For every n >= 0, exactly seven sums are prime among a(n+i) + a(n+j), 0 <= i < j < 7; lexicographically earliest such sequence of distinct nonnegative numbers.

0, 1, 2, 3, 4, 6, 24, 9, 5, 7, 11, 10, 8, 14, 12, 29, 15, 17, 13, 16, 30, 18, 23, 19, 20, 41, 45, 22, 38, 26, 25, 27, 28, 75, 21, 33, 34, 39, 31, 40, 36, 32, 35, 37, 42, 47, 49, 54, 48, 52, 53, 43, 44, 55, 84, 46, 50, 57, 51, 59, 56, 60, 71, 92, 68, 63, 83, 66, 61, 131, 62, 96, 58, 65, 102, 69, 77, 164

Offset: 0

Author

M. F. Hasler, Nov 17 2019

Keywords

• nonn

Comments

That is, there are 7 primes, counted with multiplicity, among the 21 pairwise sums of any 7 consecutive terms.

Is this a permutation of the nonnegative integers?

If so, then the restriction to [1..oo) is a permutation of the positive integers, but not the lexicographically earliest one with this property, which starts (1, 2, 3, 4, 5, 6, 89, 8, 7, 9, 10, 11, 14, 12, 17, 19, 18, 13, ...).

Crossrefs

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

Cf. A329449 (4 primes using 4 consecutive terms), A329455 (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), A329450 (0 primes using 3 terms).

Cf. A329405 ff: other variants defined for positive integers.

Programs

PARI

A329577(n,show=0,o=0,N=7,M=6,p=[],U,u=o)={for(n=o,n-1, if(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