A003608 Add 4, then reverse digits; start with 0. (Formerly M3339)

0, 4, 8, 21, 52, 65, 96, 1, 5, 9, 31, 53, 75, 97, 101, 501, 505, 905, 909, 319, 323, 723, 727, 137, 141, 541, 545, 945, 949, 359, 363, 763, 767, 177, 181, 581, 585, 985, 989, 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

Offset

0,2

Comments

Enters the cycle of length 54 given in A119031 at a(7) = 1. - M. F. Hasler, Mar 15 2022

References

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 15.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..70.

Nick Hobson, Python program for this sequence

Index entries for linear recurrences with constant coefficients, 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).

Formula

a(n + 54) = a(n) for n >= 7.

Maple

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

Mathematica

NestList[FromDigits[Reverse[IntegerDigits[#+4]]]&, 0, 70] (* Harvey P. Dale, Jan 20 2014 *)

Prog

(PARI) A003608=vector(66, i, a=if(i>1, fromdigits(Vecrev(digits(a+4))))) \\ M. F. Hasler, Mar 15 2022
(Python)
def A003608(N=66, a=0, d=4): # optional args: # terms, initial value, increment
   for _ in range(N): yield a; a=int(str(a+d)[::-1])
list(A003608()) # M. F. Hasler, Mar 15 2022

Crossrefs

All of A003608, A016081, A016082 (and possibly others) eventually reach the trajectory of 1 shown in A119031. Cf. A055198.

Sequence in context: A261031 A077921 A097076 * A248423 A319565 A129794

Adjacent sequences: A003605 A003606 A003607 * A003609 A003610 A003611

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Mira Bernstein

Extensions

Corrected by Nick Hobson, Feb 21 2007

More terms from Emeric Deutsch, Mar 07 2007

Edited by M. F. Hasler, Mar 15 2022

Status

approved