A019590 - cp's OEIS frontend

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

Offset: 1

N. J. A. Sloane

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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Index entries for characteristic functions

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).
Cf. A008683.

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

a(n) = (-1)^n*Sum_{k=0..floor(n/2)} (-1)^A010060(n-2k) mod (C(n, 2k), 2). - Paul Barry, Jan 03 2005
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
a(n) = Sum_{d|n} mu(n/d) * gcd(d,2). - Ridouane Oudra, May 30 2025

cp's OEIS Frontend

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.

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