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A134440 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.

%I A134440 #17 Mar 11 2022 12:38:07
%S A134440 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 A134440 122,61,164,82,41,154,77,208,104,52,26,13,170,85,252,126,63,244,122,
%U A134440 61,258,129,340,170,85,314,157,396,198,99,356,178,89,360,180,90,45
%N A134440 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 A134440 LFSR with primes.
%C A134440 Is it true that Lim a(n)/prime(n) < square root(3)?
%D A134440 T. Herlestam, On functions of linear shift register sequences. Springer Lecture notes in computer sciences, ISBN 978-3-540-16468-5.
%H A134440 Harvey P. Dale, <a href="/A134440/b134440.txt">Table of n, a(n) for n = 0..1000</a>
%H A134440 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 A134440 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 A134440 := proc(n)
%p A134440     option remember;
%p A134440     if n =0 then
%p A134440         1;
%p A134440     elif type(procname(n-1),'odd') then
%p A134440         procname(n-1)+ithprime(n) ;
%p A134440     else
%p A134440         procname(n-1)/2 ;
%p A134440     end if;
%p A134440 end proc: # _R. J. Mathar_, Jun 20 2021
%t A134440 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 A134440 Cf. A000040, A135287.
%K A134440 nonn
%O A134440 0,2
%A A134440 _Ctibor O. Zizka_, Jan 18 2008
%E A134440 Offset corrected by _R. J. Mathar_, Jun 20 2021