A292550 a(n) = smallest k >= 1 such that {1, 3^n, 5^n, ... , (4*k-1)^n} can be partitioned into two sets with equal sums.

1, 2, 4, 8, 10, 14, 19

Offset

0,2

Links

Table of n, a(n) for n=0..6.

Example

n = 0
1^0 = 3^0.
n = 1
1^1 + 7^1 = 3^1 + 5^1.
n = 2
1^2 + 7^2 + 11^2 + 13^2 = 3^2 + 5^2 + 9^2 + 15^2.
n = 3
1^3 + 7^3 + 11^3 + 13^3 + 19^3 + 21^3 + 25^3 + 31^3 = 3^3 + 5^3 + 9^3 + 15^3 + 17^3 + 23^3 + 27^3 + 29^3.
n = 4
1^4 + 5^4 + 13^4 + 17^4 + 19^4 + 25^4 + 27^4 + 29^4 + 31^4 + 39^4 = 3^4 + 7^4 + 9^4 + 11^4 + 15^4 + 21^4 + 23^4 + 33^4 + 35^4 + 37^4.
n = 5
1^5 + 3^5 + 7^5 + 11^5 + 17^5 + 21^5 + 33^5 + 35^5 + 37^5 + 39^5 + 41^5 + 43^5 + 51^5 + 53^5 = 5^5 + 9^5 + 13^5 + 15^5 + 19^5 + 23^5 + 25^5 + 27^5 + 29^5 + 31^5 + 45^5 + 47^5 + 49^5 + 55^5.

Crossrefs

Cf. A019568 (similar sequence).

Cf. A292476, A292496, A292522.

Sequence in context: A069879 A074330 A317626 * A024895 A250310 A288447

Adjacent sequences: A292547 A292548 A292549 * A292551 A292552 A292553

Keyword

nonn,hard,more

Author

Seiichi Manyama, Sep 18 2017

Extensions

a(5)-a(6) from Alois P. Heinz, Sep 18 2017

Status

approved