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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.
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%I #34 Feb 13 2018 00:20:06

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

%N 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.

%e n = 0

%e 1^0 = 3^0.

%e n = 1

%e 1^1 + 7^1 = 3^1 + 5^1.

%e n = 2

%e 1^2 + 7^2 + 11^2 + 13^2 = 3^2 + 5^2 + 9^2 + 15^2.

%e n = 3

%e 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.

%e n = 4

%e 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.

%e n = 5

%e 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.

%Y Cf. A019568 (similar sequence).

%Y Cf. A292476, A292496, A292522.

%K nonn,hard,more

%O 0,2

%A _Seiichi Manyama_, Sep 18 2017

%E a(5)-a(6) from _Alois P. Heinz_, Sep 18 2017