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 A077077 Trajectory of 775 under the Reverse and Add! operation carried out in base 2, written in base 10. 9
 775, 1674, 2325, 5022, 8919, 23976, 26757, 47376, 49581, 96048, 102669, 193056, 197469, 388704, 401949, 779328, 788157, 1563840, 1590333, 3131520, 3149181, 6273408, 6326397, 12554496, 12589821, 25129728, 25235709, 50274816, 50345469 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The base 2 trajectory of 775 = A075252(5) provably does not contain a palindrome. A proof can be based on the formula given below. lim_{n -> infinity} a(n)/a(n-1) = 1 for n mod 2 = 1. lim_{n -> infinity} a(n)/a(n-1) = 2 for n mod 2 = 0. Interleaving of A177843, 6*A177844, 3*A177845, 6*A177846. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 Klaus Brockhaus, On the 'Reverse and Add!' algorithm in base 2 FORMULA a(0), ..., a(5) as above; for n > 5 and n = 2 (mod 4): a(n) = 3*2^(2*k+7)+273*2^k-3 where k = (n+6)/4; n = 3 (mod 4): a(n) = 6*2^(2*k+7)-222*2^k where k = (n+5)/4; n = 0 (mod 4): a(n) = 6*2^(2*k+7)+54*2^k-3 where k = (n+4)/4; n = 1 (mod 4): a(n) = 12*2^(2*k+7)-282*2^k where k = (n+3)/4. a(n) = -a(n-1)+2*a(n-2)+2*a(n-3)+2*a(n-4)+2*a(n-5)-4*a(n-6)-4*a(n-7)-3 for n > 12; a(0), ..., a(12) as above. G.f.: (775+1674*x+1944*x^4+8910*x^5+4650*x^6-14508*x^7-19840*x^8-22644*x^9- 1860*x^10+28680*x^11+14328*x^12-2112*x^13) / ((1-x)*(1+x)*(1-2*x^2)*(1-2*x^4)). G.f. for the sequence starting at a(6): 3*(8919+15792*x-10230*x^2- 15360*x^3-15358*x^4-31696*x^5+16668*x^6+31264*x^7) / ((1-x)*(1+x)*(1-2*x^2)*(1-2*x^4)). a(n+1) = A055944(a(n)). - Reinhard Zumkeller, Apr 21 2013 EXAMPLE 775 (decimal) = 1100000111 -> 1100000111 + 1110000011 = 11010001010 = 1674 (decimal). MATHEMATICA NestWhileList[# + IntegerReverse[#, 2] &, 775,  # != IntegerReverse[#, 2] &, 1, 28] (* Robert Price, Oct 18 2019 *) PROG (PARI) trajectory(n, steps) = {local(v, k=n); for(j=0, steps, print1(k, ", "); v=binary(k); k+=sum(j=1, #v, 2^(j-1)*v[j]))}; trajectory(775, 28); (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(775, 28, 2); (Haskell) a077077 n = a077077_list !! n a077077_list = iterate a055944 775  -- Reinhard Zumkeller, Apr 21 2013 CROSSREFS Cf. A058042 (trajectory of 22 in base 2, written in base 2), A061561 (trajectory of 22 in base 2), A075253 (trajectory of 77 in base 2), A075268 (trajectory of 442 in base 2), A077076 (trajectory of 537 in base 2), A075252 (trajectory of n in base 2 does not reach a palindrome and (presumably) does not join the trajectory of any term m < n). Cf. A177843 (a(4*n)), A177844 (a(4*n+1)/6), A177845 (a(4*n+2)/3), A177846 (a(4*n+3)/6). Sequence in context: A233991 A250087 A252673 * A177845 A177843 A202893 Adjacent sequences:  A077074 A077075 A077076 * A077078 A077079 A077080 KEYWORD base,nonn AUTHOR Klaus Brockhaus, Oct 25 2002 EXTENSIONS Comment edited, three comments and formula added, g.f. edited, PARI program revised, MAGMA program and crossrefs added by Klaus Brockhaus, May 14 2010 STATUS approved

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Last modified May 6 14:16 EDT 2021. Contains 343586 sequences. (Running on oeis4.)