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%I #7 Mar 30 2012 18:38:59
%S 2,4,11,13,7,28,47,49,74,76,60,109,146,148,191,193,207,207,233,301,
%T 362,364,63,433,506,212,587,174,674,368,503,769,866,766,971,368,1082,
%U 1071,1199,1201,1322,648,1144,1453,1586,535,508,944,991,1478,2027,2029,215
%N a(n) = min { A070923(k) | n^3 < k < (n+1)^3 }.
%C Strong conjecture : for n>12, n^2/2<a(n)<n^2. Weak conjecture : a(n)>n for any n. A simple application of the weak conjecture could be to determine if the equation x^3-y^2 = A (A integer) has no solution in integers. For example the equation x^3-y^2 = 5 would have no solution in integers since a(n)>5 for n>5 and from a direct calculus, A070923(k) is different from 5, k = 1^3 to 6^3.
%C The strong conjecture does not hold for n = 23, 26, 28, 30, 36, 42, 46, 47, 48, 49, ... - Lambert Klasen (Lambert.Klasen(AT)gmx.net), Dec 17 2004
%o (PARI) for(n=1,21,s=1; while(sum(i=n^3+1,(n+1)^3-1,sign(ceil(i^(2/3))^3-i^2-s))==(n+1)^3-1-n^3,s++); print1(s,","))
%Y Cf. A070959, A070923.
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_, May 26 2002
%E More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Dec 17 2004
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