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A331527 a(n) is the least positive k such that A100274(n) - k^4 is a fifth power.

%I A331527 #13 Jan 20 2020 12:54:25
%S A331527 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 A331527 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 A331527 5,7,13,31,38,38,29,40,37,41,3,9,42,39,42,41,8,43,46
%N A331527 a(n) is the least positive k such that A100274(n) - k^4 is a fifth power.
%H A331527 Rémy Sigrist, <a href="/A331527/b331527.txt">Table of n, a(n) for n = 1..10000</a>
%H A331527 Rémy Sigrist, <a href="/A331527/a331527.gp.txt">PARI program for A331527</a>
%e A331527 The first terms, alongside A100274(n), are:
%e A331527   n   a(n)  A100274(n)
%e A331527   --  ----  ------------------
%e A331527    1     1      2 =  1^4 + 1^5
%e A331527    2     2     17 =  2^4 + 1^5
%e A331527    3     3    113 =  3^4 + 2^5
%e A331527    4     4    257 =  4^4 + 1^5
%e A331527    5     4    499 =  4^4 + 3^5
%e A331527    6     6   1297 =  6^4 + 1^5
%e A331527    7     8   4339 =  8^4 + 3^5
%e A331527    8     6   4421 =  6^4 + 5^5
%e A331527    9     7  10177 =  7^4 + 6^5
%e A331527   10    10  10243 = 10^4 + 3^5
%o A331527 (PARI) See Links section.
%Y A331527 See A331435 for similar sequences.
%Y A331527 Cf. A000584, A100274.
%K A331527 nonn
%O A331527 1,2
%A A331527 _Rémy Sigrist_, Jan 19 2020