A127397 -id:A127397 - cp's OEIS frontend

A127398 a(0)=0; a(n) = A127397(n-1)+A127397(n), which is j^k, j = any positive integer, k = any integer >= 2.

0, 1, 4, 8, 9, 16, 25, 27, 16, 8, 16, 25, 32, 25, 27, 49, 64, 81, 100, 64, 27, 25, 16, 25, 49, 64, 81, 100, 81, 49, 64, 81, 64, 49, 64, 81, 64, 49, 64, 81, 64, 49, 64, 81, 64, 49, 64, 81, 100, 121, 125, 121, 125, 121, 125, 121, 100, 81, 100, 121, 125, 144, 125, 121, 128, 121

Offset: 0

Leroy Quet, Jan 12 2007

nonn

Cf. A127397.

Extended by Ray Chandler, Jan 22 2007

A334126 a(n) is the smallest positive integer not already in the sequence such that Sum_{i=k..n} a(i) is not a perfect power for 0 < k < n; start with a(1)=1.

Original entry on oeis.org

1, 2, 3, 7, 5, 6, 17, 12, 8, 10, 4, 16, 13, 11, 15, 18, 19, 9, 14, 23, 20, 30, 22, 21, 26, 36, 29, 24, 27, 32, 25, 33, 34, 35, 28, 46, 31, 37, 47, 38, 39, 49, 41, 48, 40, 42, 50, 43, 44, 51, 45, 52, 53, 56, 54, 58, 59, 55, 62, 65, 68, 67, 57, 63, 64, 70, 61, 69

Offset: 1

Jinyuan Wang, May 10 2020

nonn

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.

Cf. A001597, A127397.

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; }

cp's OEIS Frontend

A127398 a(0)=0; a(n) = A127397(n-1)+A127397(n), which is j^k, j = any positive integer, k = any integer >= 2.

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A334126 a(n) is the smallest positive integer not already in the sequence such that Sum_{i=k..n} a(i) is not a perfect power for 0 < k < n; start with a(1)=1.

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