A009056 Numbers >= 3.

3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset: 1

Author

David W. Wilson

Keywords

• easy
• nonn

Comments

Same as Pisot sequences E(3,4), P(3,4), T(3,4). See A008776 for definitions of Pisot sequences.

Non-Fermat-exponents, positive integers n such that there are no solutions in positive integers of the equation a^n + b^n = c^n. - Tanya Khovanova, Jul 09 2011

Sums of twin primes. - Charles R Greathouse IV, Jun 21 2012

Links

• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A009005, A020739, A055998.

Programs

Mathematica

Range[3,80] (* Harvey P. Dale, Sep 26 2017 *)

PARI

a(n)=n+2 \\ Charles R Greathouse IV, Jun 21 2012

Formula

a(n) = n + 2.

From R. J. Mathar, May 26 2008: (Start)

O.g.f.: x*(3-2*x)/(1-x)^2.

a(n) = A009005(n-1), n > 2. (End)

From Elmo R. Oliveira, Oct 31 2024: (Start)

E.g.f.: exp(x)*(x + 2) - 2.

a(n) = 2*a(n-1) - a(n-2) for n > 2.

a(n) = A055998(n) - A055998(n-1) = A020739(n-1)/2. (End)