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A363759 Smallest number that can be written as a sum of a positive n-th power and a positive (n+1)-th power in 2 different ways.

%I A363759 #21 Jun 20 2023 15:01:08
%S A363759 5,17,4097,1048577,1073741825,4398046511105,72057594037927937,
%T A363759 4722366482869645213697,1237940039285380274899124225,
%U A363759 1298074214633706907132624082305025,5444517870735015415413993718908291383297
%N A363759 Smallest number that can be written as a sum of a positive n-th power and a positive (n+1)-th power in 2 different ways.
%e A363759 5 = 1^1 + 2^2 = 4^1 + 1^2.
%e A363759 17 = 3^2 + 2^3 = 4^2 + 1^3.
%e A363759 4097 = 1^3 + 8^4 = 16^3 + 1^4.
%e A363759 1048577 = 1^4 + 16^6 = 32^5 + 1^6.
%o A363759 (PARI) a(n) = my(k=1); while (!(sum(j=1, k^(1/n), (k>j^n)*ispower(k-j^n, n+1))==2), k++); k;
%Y A363759 Cf. A000051, A016078.
%K A363759 nonn
%O A363759 1,1
%A A363759 _Seiichi Manyama_, Jun 20 2023