A071069 a(n) = min { A070923(k) | n^3 < k < (n+1)^3 }.

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..53.

Prog

(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, ", "))

Crossrefs

Cf. A070959, A070923.

Sequence in context: A136993 A136992 A089694 * A116439 A018525 A102935

Adjacent sequences: A071066 A071067 A071068 * A071070 A071071 A071072

Keyword

easy,nonn

Author

Benoit Cloitre, May 26 2002

Extensions

More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Dec 17 2004

Status

approved