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A061561
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Trajectory of 22 under the Reverse and Add! operation carried out in base 2.
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20
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22, 35, 84, 105, 180, 225, 360, 405, 744, 837, 1488, 1581, 3024, 3213, 6048, 6237, 12192, 12573, 24384, 24765, 48960, 49725, 97920, 98685, 196224, 197757, 392448, 393981, 785664, 788733, 1571328, 1574397, 3144192, 3150333, 6288384, 6294525
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Sequence A058042 written in base 10. 22 is the smallest number whose base 2 trajectory does not contain a palindrome.
lim_{n -> infinity} a(n)/a(n-1) = 2 for n mod 2 = 0.
lim_{n -> infinity} a(n)/a(n-1) = 1 for n mod 2 = 1.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..500
Klaus Brockhaus, On the 'Reverse and Add!' algorithm in base 2
Index entries for sequences related to Reverse and Add!
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FORMULA
| a(0) = 22; a(1) = 35; for n > 1 and n = 2 (mod 4): a(n) = 6*2^(2*k)-3*2^k where k = (n+6)/4; n = 3 (mod 4): a(n) = 6*2^(2*k)+3*2^k-3 where k = (n+5)/4; n = 0 (mod 4): a(n) = 12*2^(2*k)-3*2^k where k = (n+4)/4; n = 1 (mod 4): a(n) = 12*2^(2*k)+9*2^k-3 where k = (n+3)/4. [From Klaus Brockhaus, Sep 05 2002]
G.f.: (22+35*x+18*x^2-72*x^4-90*x^5-48*x^6-60*x^7+80*x^8+112*x^9) / ((1-x)*(1+x)*(1-2*x^2)*(1-2*x^4)) [From Klaus Brockhaus, Sep 05 2002, edited Dec 09 2009]
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PROG
| (ARIBAS) m := 22; stop := 36; c := 0; while c < stop do write(m, ", "); k := bit_length(m); rev := 0; for i := 0 to k-1 do if bit_test(m, i) then rev := bit_set(rev, k-1-i); end; end; inc(c); m := m+rev; end; .
(PARI) {m=22; stop=36; c=0; while(c<stop, print1(k=m, ", "); rev=0; while(k>0, d=divrem(k, 2); k=d[1]; rev=2*rev+d[2]); c++; m=m+rev)}
(MAGMA) trajectory:=function(init, steps, base) a:=init; S:=[a]; for n in [1..steps] do a+:=Seqint(Reverse(Intseq(a, base)), base); Append(~S, a); end for; return S; end function; trajectory(22, 35, 2);
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CROSSREFS
| Cf. A035522 (trajectory of 1 in base 2), A058042 (trajectory of 22 in base 2, written in base 2), A075253 (trajectory of 77 in base 2), A075268 (trajectory of 442 in base 2), A077076 (trajectory of 537 in base 2), A077077 (trajectory of 775 in base 2), A066059 (trajectory of n in base 2 (presumably) does not reach a palindrome), A075252 (trajectory of n in base 2 does not reach a palindrome and (presumably) does not join the trajectory of any term m < n), A075153 (trajectory of 318 in base 4).
Cf. A171470 (a(4*n)/2), A171471 (a(4*n+1)), A171472 (a(4*n+2)/12), A171473 (a(4*n+3)/3).
Sequence in context: A124317 A159518 A100039 * A167277 A084141 A082261
Adjacent sequences: A061558 A061559 A061560 * A061562 A061563 A061564
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KEYWORD
| nonn,base
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 18 2001
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EXTENSIONS
| More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 27 2001
G.f. and crossrefs edited, two comments and MAGMA program added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 09 2009
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