A134440 - OEIS

%I #17 Mar 11 2022 12:38:07

%S 1,3,6,3,10,5,18,9,28,14,7,38,19,60,30,15,68,34,17,84,42,21,100,50,25,

%T 122,61,164,82,41,154,77,208,104,52,26,13,170,85,252,126,63,244,122,

%U 61,258,129,340,170,85,314,157,396,198,99,356,178,89,360,180,90,45

%N a(0)=1; for n > 0, a(n) = a(n-1) + prime(n) if a(n-1) is odd, else a(n) = a(n-1)/2.

%C LFSR with primes.

%C Is it true that Lim a(n)/prime(n) < square root(3)?

%D T. Herlestam, On functions of linear shift register sequences. Springer Lecture notes in computer sciences, ISBN 978-3-540-16468-5.

%H Harvey P. Dale, <a href="/A134440/b134440.txt">Table of n, a(n) for n = 0..1000</a>

%H Georg Schmidt and Vladimir R. Sidorenko, <a href="https://arxiv.org/abs/cs/0605044">Linear Shift-Register Synthesis for Multiple Sequences of Varying Length</a>, arXiv:cs/0605044 [cs.IT], 2001.

%H Boaz Tsaban and Uzi Vishne, <a href="https://arxiv.org/abs/cs/0304010">Efficient linear feedback shift registers with maximal period</a>, arXiv:cs/0304010 [cs.CR], 2003.

%p A134440 := proc(n)

%p     option remember;

%p     if n =0 then

%p         1;

%p     elif type(procname(n-1),'odd') then

%p         procname(n-1)+ithprime(n) ;

%p     else

%p         procname(n-1)/2 ;

%p     end if;

%p end proc: # _R. J. Mathar_, Jun 20 2021

%t nxt[{n_,a_}]:={n+1,If[OddQ[a],a+Prime[n+1],a/2]}; Transpose[ NestList[ nxt,{0,1},70]][[2]] (* _Harvey P. Dale_, Jan 12 2016 *)

%Y Cf. A000040, A135287.

%K nonn

%O 0,2

%A _Ctibor O. Zizka_, Jan 18 2008

%E Offset corrected by _R. J. Mathar_, Jun 20 2021