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A019590 Fermat's Last Theorem: a(n) = 1 if x^n + y^n = z^n has a nontrivial solution in integers, otherwise a(n) = 0. 115
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)



a(n) is the Hankel transform of A000045(n), n>=1 (Fibonacci numbers). See A055879 for the definition of Hankel transform. - Wolfdieter Lang, Jan 23 2007

1, -1, 0, 0, 0, ... is the convolutional inverse of the all-ones sequence. - Tanya Khovanova, Jun 29 2007

Also parity of the Euler totient function A000010. - Omar E. Pol, Jan 15 2012

a(n-1) gives the row sums of A048994. - Wolfdieter Lang, May 09 2017

Decimal expansion of 11/10. - Franklin T. Adams-Watters, Mar 08 2019


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Table of n, a(n) for n=1..96.

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Index entries for characteristic functions


a(n) = (-1)^n*Sum_{k=0..floor(n/2)} (-1)^A010060(n-2k) mod (C(n, 2k), 2). - Paul Barry, Jan 03 2005

a(n) = 1 - ((n+2) mod (n+1)) + (n!^2 mod (n+1))*((n+1)!^2 mod (n+2)). - Paolo P. Lava, Aug 29 2007

a(n) = (n-1)! mod 2, with n >= 1. - Paolo P. Lava, Feb 15 2008

a(n+1) = (1/2)*(1+(-1)^n)*a(n), with a(0)=1. - Paolo P. Lava, Apr 16 2008

Euler transform of length 2 sequence [1, -1]. - Michael Somos, Jul 05 2009

a(n) is multiplicative with a(2) = 1, a(2^e) = 0 if e > 1, a(p^e) = 0^e if p > 2. - Michael Somos, Jul 05 2009

G.f.: x + x^2 = x * (1 - x^2) / (1 - x). - Michael Somos, Jul 05 2009

Dirichlet g.f.: 1 + 2^(-s). - Michael Somos, Jul 05 2009

a(n) = A000035(A000010(n)). - Omar E. Pol, Oct 28 2013


(PARI) {a(n) = (n==1) + (n==2)}; /* Michael Somos, Jul 05 2009 */


Cf. A000004, A000007, A010051, A012450.

INVERT transform gives Fibonacci numbers, A000045.

Convolution inverse of A062157. Dirichlet convolution inverse of A154269.

Cf. A229382, A229383 (near-miss counterexamples to FLT).

Cf. A048994 (row sums).

Sequence in context: A134323 A060576 A261012 * A154955 A240356 A240354

Adjacent sequences:  A019587 A019588 A019589 * A019591 A019592 A019593




N. J. A. Sloane



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Last modified September 28 00:09 EDT 2022. Contains 357063 sequences. (Running on oeis4.)