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Numbers k such that both k and k+1 are sums of two positive cubes.
4

%I #24 May 20 2018 12:44:51

%S 854,4940,9603,10744,17919,29743,62558,79001,133273,164304,193192,

%T 205406,214984,242648,263871,378936,431999,447336,488375,517427,

%U 610687,731158,762047,1000511,1061550,1125207,1134124,1157632,1158137,1179520

%N Numbers k such that both k and k+1 are sums of two positive cubes.

%C There are 664 terms < 8*10^9, a(664)=7999968373. - _Zak Seidov_, Jul 24 2009

%C This is an infinite sequence. To see why, consider the (N,N+1) pair N = 16*k^6 - 12*k^4 + 6*k^2 - 2 = (2*k^2 - k - 1)^3 + (2*k^2 + k -1)^3 and N + 1 = 16*k^6 - 12*k^4 + 6*k^2 - 1 = (2*k^2)^3 + (2*k^2 - 1)^3. - _Ant King_, Sep 20 2013

%H Zak Seidov, <a href="/A085323/b085323.txt">Table of n, a(n) for n = 1..664</a>

%e 854 = 9^3 + 5^3 and 855 = 8^3 + 7^3;

%e 4940 = 17^3 + 3^3 and 4941 = 13^3 + 14^3.

%t {m=100, k=3, m^k}; t=Union[Flatten[Table[Table[w^k+q^k, {w, 1, m}], {q, 1, m}]]]; dt=Delete[ -RotateRight[t]+t, 1]; p=Part[t, Flatten[Position[dt, 1]]]; p

%Y Cf. A003325.

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 01 2003

%E Corrected and extended by _Zak Seidov_, Jul 24 2009

%E Name and Example edited by _Jon E. Schoenfield_, Jul 29 2017