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Search: id:A071069
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| 2, 4, 11, 13, 7, 28, 47, 49, 74, 76, 60, 109, 146, 148, 191, 193, 207, 207, 233, 301, 362, 364, 63, 433, 506, 212, 587, 174, 674, 368, 503, 769, 866, 766, 971, 368, 1082, 1071, 1199, 1201, 1322, 648, 1144, 1453, 1586, 535, 508, 944, 991, 1478, 2027, 2029, 215
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OFFSET
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1,1
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COMMENT
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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.
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
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PROGRAM
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(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, ", "))
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CROSSREFS
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Cf. A070959, A070923.
Sequence in context: A136993 A136992 A089694 this_sequence A116439 A018525 A102935
Adjacent sequences: A071066 A071067 A071068 this_sequence A071070 A071071 A071072
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), May 26 2002
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EXTENSIONS
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More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Dec 17 2004
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