cp's OEIS Frontend

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.

%I A329577 #10 Nov 28 2019 11:02:51
%S A329577 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,
%T A329577 45,22,38,26,25,27,28,75,21,33,34,39,31,40,36,32,35,37,42,47,49,54,48,
%U A329577 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
%N 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.
%C A329577 That is, there are 7 primes, counted with multiplicity, among the 21 pairwise sums of any 7 consecutive terms.
%C A329577 Is this a permutation of the nonnegative integers?
%C A329577 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, ...).
%o A329577 (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<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
%Y A329577 Cf. A329425 (6 primes using 5 consecutive terms), A329566 (6 primes using 6 consecutive terms).
%Y A329577 Cf. A329449 (4 primes using 4 consecutive terms), A329455 (4 primes using 5 consecutive terms).
%Y A329577 Cf. A329454 (3 primes using 4 consecutive terms), A329455 (3 primes using 5 consecutive terms).
%Y A329577 Cf. A329411 (2 primes using 3 consecutive terms), A329452 (2 primes using 4 consecutive terms), A329453 (2 primes using 5 consecutive terms).
%Y A329577 Cf. A329333 (1 odd prime using 3 terms), A329450 (0 primes using 3 terms).
%Y A329577 Cf. A329405 ff: other variants defined for positive integers.
%K A329577 nonn
%O A329577 0,3
%A A329577 _M. F. Hasler_, Nov 17 2019