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A331524 a(n) is the least positive k such that A006686(n) - k^8 is an eighth power.

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%I A331524 #15 Jan 20 2020 12:53:57
%S A331524 1,1,1,5,3,7,2,8,3,8,9,13,4,4,17,7,17,2,8,3,5,20,7,11,17,8,23,19,10,
%T A331524 20,3,11,17,10,22,19,14,22,17,21,25,11,13,23,27,8,32,25,33,6,25,35,7,
%U A331524 23,31,10,37,16,18,39,5,7,42,41,30,36,5,11,8,18,30,36
%N A331524 a(n) is the least positive k such that A006686(n) - k^8 is an eighth power.
%H A331524 Rémy Sigrist, <a href="/A331524/b331524.txt">Table of n, a(n) for n = 1..10000</a>
%H A331524 Rémy Sigrist, <a href="/A331524/a331524_1.gp.txt">PARI program for A331524</a>
%e A331524 The first terms, alongside A006686(n), are:
%e A331524   n   a(n)  A006686(n)
%e A331524   --  ----  -----------------------
%e A331524    1     1           2 = 1^8 +  1^8
%e A331524    2     1         257 = 1^8 +  2^8
%e A331524    3     1       65537 = 1^8 +  4^8
%e A331524    4     5     2070241 = 5^8 +  6^8
%e A331524    5     3   100006561 = 3^8 + 10^8
%e A331524    6     7   435746497 = 7^8 + 12^8
%e A331524    7     2   815730977 = 2^8 + 13^8
%e A331524    8     8   832507937 = 8^8 + 13^8
%e A331524    9     3  1475795617 = 3^8 + 14^8
%e A331524   10     8  2579667841 = 8^8 + 15^8
%o A331524 (PARI) See Links section.
%Y A331524 See A331435 for similar sequences.
%Y A331524 Cf. A001016, A006686.
%K A331524 nonn
%O A331524 1,4
%A A331524 _Rémy Sigrist_, Jan 19 2020