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Search: id:A075253
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| A075253 |
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Trajectory of 77 under the Reverse and Add! operation carried out in base 2. |
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+0
8
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| 77, 166, 267, 684, 897, 1416, 1557, 2904, 3333, 5904, 6189, 11952, 12813, 24096, 24669, 48480, 50205, 97344, 98493, 195264, 198717, 391296, 393597, 783744, 790653, 1569024, 1573629, 3140352, 3154173, 6283776, 6292989, 12572160
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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22 is the smallest number whose base 2 trajectory (A061561) provably does not contain a palindrome. 77 is the next number (cf. A075252) with a completely different trajectory which has this property. A proof along the lines of Klaus Brockhaus, On the 'Reverse and Add!' algorithm in base 2, can be based on the formula given below.
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LINKS
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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
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a(0) = 77; a(1) = 166; a(2) = 267; for n > 2 and n = 3 (mod 4): a(n) = 48*2^(2*k)-21*2^k where k = (n+5)/4; n = 0 (mod 4): a(n) = 48*2^(2*k)+33*2^k-3 where k = (n+4)/4; n = 1 (mod 4): a(n) = 96*2^(2*k)-30*2^k where k = (n+3)/4; n = 2 (mod 4): a(n) = 96*2^(2*k)+6*2^k-3 where k = (n+2)/4. G.f.: -(504*x^10+632*x^9-44*x^8-348*x^7-672*x^6-636*x^5+96*x^4+186*x^3+36*x^2+166*x+77)/((x-1)*(x+1)*(2*x^2-1)*(2*x^4-1)).
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EXAMPLE
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267 (decimal) = 100001011 -> 100001011 + 110100001 = 1010101100 = 684 (decimal).
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PROGRAM
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(PARI) {m=77; stop=34; 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)}
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CROSSREFS
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Cf. A058042, A061561, A075252.
Sequence in context: A113945 A044328 A044709 this_sequence A046513 A043518 A044409
Adjacent sequences: A075250 A075251 A075252 this_sequence A075254 A075255 A075256
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KEYWORD
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base,nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 10 2002
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