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A141326 Subsequence of 'Fermat near misses' which is generated by a simple formula based on the cubic binomial expansion along with formulas for the corresponding terms in the expression, x^3 + y^3 = z^3 + 1. 3
12, 150, 738, 2316, 5640, 11682, 21630, 36888, 59076, 90030, 131802, 186660, 257088, 345786, 455670, 589872, 751740, 944838, 1172946, 1440060 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Note that the given formulas generate 1 + 12^3 = 9^3 + 10^3 = 1729 for n=1. In this case b(1) < c(1), whereas b(n) > c(n) for n > 1.

Contribution from Lewis Mammel (l_mammel(AT)att.net), Aug 21 2008: (Start)

In Ramanujan's parametric equation:

(ax+y)^3 + (b+x^2y)^3 = (bx+y)^3 + (a+x^2y)^3

where

a^2 + ab + b^2 = 3xy^2

This sequence is obtained by setting a=0, y=1 and finding the solution to b^2=3x:

b=3n, x=3n^2 (End)

LINKS

Table of n, a(n) for n=1..20.

Wolfram Mathworld, Diophantine Equation--3rd Powers [From Lewis Mammel (l_mammel(AT)att.net), Aug 21 2008]

FORMULA

With a(n) = 9*n^4 + 3*n b(n) = 9*n^4 c(n) = 9*n^3 + 1 1 + a(n)^3 = b(n)^3 + c(n)^3, by substitution and expansion

With a(n) = 9*n^4 + 3*n, b(n) = 9*n^4 and c(n) = 9*n^3 + 1, we have 1 + a(n)^3 = b(n)^3 + c(n)^3, by substitution and expansion [From Lew Mammel (l_mammel(AT)att.net), Aug 09 2008]

CROSSREFS

Cf. A050791, A050792, A050793, A050794.

Sequence in context: A057572 A114106 A015610 * A154733 A305544 A056351

Adjacent sequences:  A141323 A141324 A141325 * A141327 A141328 A141329

KEYWORD

easy,nonn

AUTHOR

Lewis Mammel (l_mammel(AT)att.net), Aug 03 2008

STATUS

approved

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Last modified October 15 10:46 EDT 2019. Contains 328026 sequences. (Running on oeis4.)