|
%I M3339 #29 Mar 16 2022 02:59:27
%S 0,4,8,21,52,65,96,1,5,9,31,53,75,97,101,501,505,905,909,319,323,723,
%T 727,137,141,541,545,945,949,359,363,763,767,177,181,581,585,985,989,
%U 399,304,803,708,217,122,621,526,35,93,79,38,24,82,68,27,13,71,57,16,2,6,1,5,9,31,53,75,97,101,501,505
%N Add 4, then reverse digits; start with 0.
%C Enters the cycle of length 54 given in A119031 at a(7) = 1. - _M. F. Hasler_, Mar 15 2022
%D J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 15.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Nick Hobson, <a href="/A003608/a003608.py.txt">Python program for this sequence</a>
%H <a href="/index/Rec#order_54">Index entries for linear recurrences with constant coefficients</a>, signature (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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F a(n + 54) = a(n) for n >= 7.
%p rev:=proc(n) local nn, nnn: nn:=convert(n,base,10): add(nn[nops(nn)+1-j]*10^(j-1),j=1..nops(nn)) end: a[0]:=0: for n from 1 to 70 do a[n]:=rev(a[n-1]+4) od: seq(a[n],n=0..70); # _Emeric Deutsch_, Mar 07 2007
%t NestList[FromDigits[Reverse[IntegerDigits[#+4]]]&,0,70] (* _Harvey P. Dale_, Jan 20 2014 *)
%o (PARI) A003608=vector(66, i, a=if(i>1,fromdigits(Vecrev(digits(a+4))))) \\ _M. F. Hasler_, Mar 15 2022
%o (Python)
%o def A003608(N=66, a=0, d=4): # optional args: # terms, initial value, increment
%o for _ in range(N): yield a; a=int(str(a+d)[::-1])
%o list(A003608()) # _M. F. Hasler_, Mar 15 2022
%Y All of A003608, A016081, A016082 (and possibly others) eventually reach the trajectory of 1 shown in A119031. Cf. A055198.
%K nonn,base
%O 0,2
%A _N. J. A. Sloane_, _Mira Bernstein_
%E Corrected by Nick Hobson, Feb 21 2007
%E More terms from _Emeric Deutsch_, Mar 07 2007
%E Edited by _M. F. Hasler_, Mar 15 2022
|
