A000038 - OEIS

%I M0004 #60 Oct 23 2024 14:34:58

%S 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 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,

%U 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

%N Twice A000007.

%C Multiplicative with a(p^e) = 0. - _Mitch Harris_, Jun 09 2005

%C Also decimal expansion of 1/5, with keyword cons. - _Wolfdieter Lang_, Jan 19 2023

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H James Spahlinger, <a href="/A000038/b000038.txt">Table of n, a(n) for n = 0..10000</a>

%H Norman L. de Forest, <a href="http://www.gutenberg.org/ebooks/3651">The Square Root of 4 to a Million Places</a>, Project Gutenberg EBook 3651, 2003.

%H Daniele A. Gewurz and Francesca Merola, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL6/Gewurz/gewurz5.html">Sequences realized as Parker vectors of oligomorphic permutation groups</a>, J. Integer Seqs., Vol. 6, 2003.

%H Chai Wah Wu, <a href="https://arxiv.org/abs/1805.07431">Can machine learning identify interesting mathematics? An exploration using empirically observed laws</a>, arXiv:1805.07431 [cs.LG], 2018.

%H Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, <a href="https://ceur-ws.org/Vol-3792/paper19.pdf">Integer sequences from k-iterated line digraphs</a>, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2. See p. 6.

%F a(n) = 2*A000007(n) = (-1)^A000040(n) + 1. - _Juri-Stepan Gerasimov_, Oct 29 2009

%t PadRight[{2}, 104] (* or *)

%t Array[(-1)^Prime@ # + 1 &, 105] (* _Michael De Vlieger_, Aug 15 2018 *)

%o (Haskell)

%o a000038 n = 2 * a000007 n -- _James Spahlinger_, Oct 08 2012

%o (PARI) a(n)=if(n,0,2) \\ _Charles R Greathouse IV_, Oct 09 2012

%Y Cf. A007395, A000007.

%K easy,nonn,mult

%O 0,1

%A _N. J. A. Sloane_