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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.
1
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
0,2
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
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.
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 *)
CROSSREFS
Sequence in context: A055373 A263333 A328371 * A129529 A298263 A128503
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Jan 18 2008
EXTENSIONS
Offset corrected by R. J. Mathar, Jun 20 2021
STATUS
approved