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A085322 Terms m of A003337 such that m+1 is also in A003337. I.e., smaller one of two consecutive numbers, both equal to a sum of three 4th powers.

%I A085322 #19 Mar 08 2025 06:00:56
%S A085322 4802,7202,10257,14802,15522,38577,45602,57122,57202,76832,86002,
%T A085322 90337,94817,109777,112162,116177,131697,135712,136897,155617,163697,
%U A085322 171137,188577,243777,260642,284562,296882,332417,388962,390962,391922,459457,474402,617057,637712
%N A085322 Terms m of A003337 such that m+1 is also in A003337. I.e., smaller one of two consecutive numbers, both equal to a sum of three 4th powers.
%H A085322 Amiram Eldar, <a href="/A085322/b085322.txt">Table of n, a(n) for n = 1..89</a> (calculated from the b-file at A003337)
%e A085322 Distance of closest neighbors in A003337 equals 1: 7202 = 6561 + 625 + 16 and 7203 = 2401 + 2401 + 2401 are corresponding neighbors, so 7202 is a term.
%t A085322 {m=25, k=4, m^k} t=Union[Flatten[Table[Table[Table[w^k+q^k+t^k, {w, 1, m}], {q, 1, m}], {t, 1, m}]]] dt=Delete[ -RotateRight[t]+t, 1]; Part[t, Flatten[Position[dt, 1]]]
%t A085322 Select[Partition[Union[Total/@Tuples[Range[25]^4,3]],2,1],#[[2]]-#[[1]] == 1&][[All,1]] (* _Harvey P. Dale_, Jul 31 2020 *)
%Y A085322 Cf. A003337, A003327-A003399, A085321.
%K A085322 nonn
%O A085322 1,1
%A A085322 _Labos Elemer_, Jul 01 2003
%E A085322 More terms from _Amiram Eldar_, Mar 08 2025