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A331435 a(n) is the least positive k such that A028916(n) - k^2 is a fourth power.

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%I A331435 #29 Jan 20 2020 12:52:34
%S A331435 1,2,1,6,5,4,10,11,10,14,15,1,14,5,9,20,21,24,19,4,6,26,26,12,14,29,
%T A331435 16,31,29,22,24,31,34,1,26,5,28,35,40,19,41,39,44,38,29,45,42,4,6,35,
%U A331435 51,16,46,20,51,54,55,56,56,30,52,54,34,36,56,58,40,9,11
%N A331435 a(n) is the least positive k such that A028916(n) - k^2 is a fourth power.
%H A331435 Rémy Sigrist, <a href="/A331435/b331435.txt">Table of n, a(n) for n = 1..10000</a>
%H A331435 Rémy Sigrist, <a href="/A331435/a331435.gp.txt">PARI program for A331435</a>
%H A331435 Wikipedia, <a href="http://en.wikipedia.org/wiki/Friedlander%E2%80%93Iwaniec_theorem">Friedlander-Iwaniec theorem</a>
%e A331435 The first terms, alongside A028916(n), are:
%e A331435   n   a(n)  A028916(n)
%e A331435   --  ----  ----------------
%e A331435    1     1    2 =  1^2 + 1^4
%e A331435    2     2    5 =  2^2 + 1^4
%e A331435    3     1   17 =  1^2 + 2^4
%e A331435    4     6   37 =  6^2 + 1^4
%e A331435    5     5   41 =  5^2 + 2^4
%e A331435    6     4   97 =  4^2 + 3^4
%e A331435    7    10  101 = 10^2 + 1^4
%e A331435    8    11  137 = 11^2 + 2^4
%e A331435    9    10  181 = 10^2 + 3^4
%e A331435   10    14  197 = 14^2 + 1^4
%o A331435 (PARI) See Links section.
%Y A331435 See A002331, A331521, A331522, A331523, A331524, A331525, A331526 and A331527 for similar sequences.
%Y A331435 Cf. A000583, A028916.
%K A331435 nonn
%O A331435 1,2
%A A331435 _Rémy Sigrist_, Jan 18 2020