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A331521 a(n) is the least positive k such that A002645(n) - k^4 is a fourth power.

%I A331521 #15 Jan 20 2020 12:53:23
%S A331521 1,1,2,1,3,2,4,1,2,4,6,3,5,2,8,7,2,4,6,9,4,10,5,12,8,1,3,5,13,11,2,4,
%T A331521 14,5,7,11,14,2,6,8,10,16,12,1,3,9,14,10,17,16,2,4,8,15,10,17,1,7,11,
%U A331521 13,18,6,8,12,3,7,19,9,11,2,19,16,1,9,13,12,23
%N A331521 a(n) is the least positive k such that A002645(n) - k^4 is a fourth power.
%H A331521 Rémy Sigrist, <a href="/A331521/b331521.txt">Table of n, a(n) for n = 1..10000</a>
%H A331521 Rémy Sigrist, <a href="/A331521/a331521_1.gp.txt">PARI program for A331521</a>
%e A331521 The first terms, alongside A002645(n), are:
%e A331521   n   a(n)  A002645(n)
%e A331521   --  ----  ----------------
%e A331521    1     1     2 = 1^4 + 1^4
%e A331521    2     1    17 = 1^4 + 2^4
%e A331521    3     2    97 = 2^4 + 3^4
%e A331521    4     1   257 = 1^4 + 4^4
%e A331521    5     3   337 = 3^4 + 4^4
%e A331521    6     2   641 = 2^4 + 5^4
%e A331521    7     4   881 = 4^4 + 5^4
%e A331521    8     1  1297 = 1^4 + 6^4
%e A331521    9     2  2417 = 2^4 + 7^4
%e A331521   10     4  2657 = 4^4 + 7^4
%o A331521 (PARI) See Links section.
%Y A331521 See A331435 for similar sequences.
%Y A331521 Cf. A000583, A002645.
%K A331521 nonn
%O A331521 1,3
%A A331521 _Rémy Sigrist_, Jan 19 2020