OFFSET
1,2
COMMENTS
I conjecture that every number eventually appears.
Let b(1) = 1; b(2*m) is the least positive integer not occurring earlier in b(i), i=1..2*m-2; b(2*m-1) is the least positive integer not already in {b(n)} such that Sum_{i=j..2*m-1} b(i) and Sum_{i=k..2*m} b(i) are not perfect powers for 0 < j < 2*m-1 and 0 < k < 2*m. Then {b(n)} is a permutation of the positive integers such that Sum_{i=k..m} b(i) is not a perfect power for any 0 < k < m.
PROG
(PARI) lista(nn) = {my(k, s, v=vector(nn)); v[1]=1; for(n=2, nn, k=s=2; while(vecsearch(vecsort(v), k) || sum(i=1, n-1, ispower(s+=v[n-i])), s=k++); v[n]=k); v; }
CROSSREFS
KEYWORD
nonn
AUTHOR
Jinyuan Wang, May 10 2020
STATUS
approved