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.

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, 122, 61, 164, 82, 41, 154, 77, 208, 104, 52, 26, 13, 170, 85, 252, 126, 63, 244, 122, 61, 258, 129, 340, 170, 85, 314, 157, 396, 198, 99, 356, 178, 89, 360, 180, 90, 45

Offset: 0

Author

Ctibor O. Zizka, Jan 18 2008

Keywords

• nonn

Comments

LFSR with primes.

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

References

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Georg Schmidt and Vladimir R. Sidorenko, Linear Shift-Register Synthesis for Multiple Sequences of Varying Length, arXiv:cs/0605044 [cs.IT], 2001.
• Boaz Tsaban and Uzi Vishne, Efficient linear feedback shift registers with maximal period, arXiv:cs/0304010 [cs.CR], 2003.

Crossrefs

Cf. A000040, A135287.

Programs

Maple

A134440 := proc(n)
    option remember;
    if n =0 then
        1;
    elif type(procname(n-1),'odd') then
        procname(n-1)+ithprime(n) ;
    else
        procname(n-1)/2 ;
    end if;
end proc: # R. J. Mathar, Jun 20 2021

Mathematica

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 *)

Extensions

Offset corrected by R. J. Mathar, Jun 20 2021