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A331523 a(n) is the least positive k such that A100271(n) - k^3 is a fourth power.

%I A331523 #14 Jan 20 2020 12:53:47
%S A331523 1,1,3,2,1,3,7,8,7,1,13,6,15,15,12,16,16,2,10,20,18,21,7,16,9,22,13,
%T A331523 22,23,24,20,10,25,12,25,22,26,27,11,26,28,30,27,31,22,31,34,30,35,36,
%U A331523 28,31,37,8,37,16,27,36,35,40,1,3,13,31,37,28,33,42,21
%N A331523 a(n) is the least positive k such that A100271(n) - k^3 is a fourth power.
%H A331523 Rémy Sigrist, <a href="/A331523/b331523.txt">Table of n, a(n) for n = 1..10000</a>
%H A331523 Rémy Sigrist, <a href="/A331523/a331523.gp.txt">PARI program for A331523</a>
%e A331523 The first terms, alongside A100271(n), are:
%e A331523   n   a(n)  A100271(n)
%e A331523   --  ----  ----------------
%e A331523    1     1     2 = 1^3 + 1^4
%e A331523    2     1    17 = 1^3 + 2^4
%e A331523    3     3    43 = 3^3 + 2^4
%e A331523    4     2    89 = 2^3 + 3^4
%e A331523    5     1   257 = 1^3 + 4^4
%e A331523    6     3   283 = 3^3 + 4^4
%e A331523    7     7   359 = 7^3 + 2^4
%e A331523    8     8   593 = 8^3 + 3^4
%e A331523    9     7   599 = 7^3 + 4^4
%e A331523   10     1  1297 = 1^3 + 6^4
%o A331523 (PARI) See Links section.
%Y A331523 See A331435 for similar sequences.
%Y A331523 Cf. A000583, A100271.
%K A331523 nonn
%O A331523 1,3
%A A331523 _Rémy Sigrist_, Jan 19 2020