

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.


5



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
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OFFSET

0,3


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, ...).


LINKS

Table of n, a(n) for n=0..77.


PROG

(PARI) A329577(n, show=0, o=0, N=7, M=6, p=[], U, u=o)={for(n=o, n1, if(show>0, print1(o", "), show<0, listput(L, o)); U+=1<<(ou); U>>=u+u+=valuation(U+1, 2); p=concat(if(#p>=M, p[^1], p), o); my(c=Nsum(i=2, #p, sum(j=1, i1, 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, ku) sum(i=1, #p, isprime(p[i]+k))!=c[o=k, break])); show&&print([u]); o} \\ optional args: show=1: print a(o..n1), 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. 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.
Sequence in context: A274238 A115035 A219048 * A217442 A065199 A249156
Adjacent sequences: A329574 A329575 A329576 * A329578 A329579 A329580


KEYWORD

nonn


AUTHOR

M. F. Hasler, Nov 17 2019


STATUS

approved



