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a(n) is the least positive k such that A100274(n) - k^4 is a fifth power.
2

%I #13 Jan 20 2020 12:54:25

%S 1,2,3,4,4,6,8,6,7,10,2,8,16,17,11,20,20,20,12,22,22,7,18,24,24,4,14,

%T 23,28,4,8,29,16,30,29,30,31,5,7,9,19,30,33,26,23,34,34,6,35,36,35,37,

%U 5,7,13,31,38,38,29,40,37,41,3,9,42,39,42,41,8,43,46

%N a(n) is the least positive k such that A100274(n) - k^4 is a fifth power.

%H Rémy Sigrist, <a href="/A331527/b331527.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A331527/a331527.gp.txt">PARI program for A331527</a>

%e The first terms, alongside A100274(n), are:

%e n a(n) A100274(n)

%e -- ---- ------------------

%e 1 1 2 = 1^4 + 1^5

%e 2 2 17 = 2^4 + 1^5

%e 3 3 113 = 3^4 + 2^5

%e 4 4 257 = 4^4 + 1^5

%e 5 4 499 = 4^4 + 3^5

%e 6 6 1297 = 6^4 + 1^5

%e 7 8 4339 = 8^4 + 3^5

%e 8 6 4421 = 6^4 + 5^5

%e 9 7 10177 = 7^4 + 6^5

%e 10 10 10243 = 10^4 + 3^5

%o (PARI) See Links section.

%Y See A331435 for similar sequences.

%Y Cf. A000584, A100274.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jan 19 2020