A329579 For every n >= 0, exactly nine 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, 5, 20, 9, 10, 8, 33, 11, 6, 50, 21, 17, 56, 12, 47, 14, 26, 7, 125, 15, 24, 83, 54, 66, 13, 35, 22, 18, 19, 48, 23, 31, 28, 30, 25, 16, 36, 42, 121, 29, 43, 37, 46, 70, 72, 60, 27, 79, 67, 40, 34, 39, 32, 69, 38, 41, 44, 45, 51, 58, 62, 86, 52, 53, 105, 171, 65, 74, 146, 68, 63, 123, 76

Offset

0,3

Comments

That is, there are 9 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 maybe not the lexicographically earliest one with this property.

Links

Table of n, a(n) for n=0..76.

Prog

(PARI) A329579(n, show=0, o=0, N=9, 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<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||[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; o=1: start at a(1)=1; N, M: find N primes using M+1 terms

Crossrefs

Cf. A329577 (7 primes using 7 consecutive terms), A329566 (6 primes using 6 consecutive terms), A329449 (4 primes using 4 consecutive terms).

Cf. A329425 (6 primes using 5 consecutive terms), A329455 (4 primes using 5 consecutive terms), A329455 (3 primes using 5 consecutive terms), A329453 (2 primes using 5 consecutive terms), A329452 (2 primes using 4 consecutive terms).

Cf. A329454 (3 primes using 4 consecutive terms), A329411 (2 primes using 3 consecutive terms), A329333 (1 odd prime using 3 terms), A329450 (0 primes using 3 terms).

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

Sequence in context: A333993 A362064 A342617 * A024635 A217679 A248901

Adjacent sequences: A329576 A329577 A329578 * A329580 A329581 A329582

Keyword

nonn

Author

M. F. Hasler, Nov 17 2019

Status

approved