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First difference sequence of A003349, i.e., consecutive differences between those consecutive numbers which are sums of four 5th powers.
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%I #10 Jul 29 2017 13:29:11

%S 31,31,31,31,118,31,31,31,149,31,31,180,31,211,55,31,31,31,149,31,31,

%T 180,31,211,297,31,31,180,31,211,539,31,24,31,31,31,94,55,31,31,180,

%U 31,211,242,55,31,31,180,31,211,539,31,211,781,55,31,31,180,31,211,539,31

%N First difference sequence of A003349, i.e., consecutive differences between those consecutive numbers which are sums of four 5th powers.

%e 35 = 1 + 1 + 1 + 32, 66 = 32 + 32 + 1 + 1, a(1) = 66 - 33 = 31.

%e Certain differences occur rather consequently like 31, 55, 113, 180, 207, 211, 539, etc.;

%e Distance of closest observed neighbors equals 2 like those of 33858 and 33856.

%t {m=12, k=5, m^k}; t=Union[Flatten[Table[Table[Table[Table[w^k+q^k+t^k+u^k, {w, 1, m}], {q, 1, m}], {t, 1, m}], {u, 1, m}]]]; Length[t]; dt=Delete[ -RotateRight[t]+t, 1]; Sort[dt]

%Y Cf. A003349, A003327-A003399.

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 01 2003