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Search: id:A077076
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| A077076 |
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Trajectory of 537 under the Reverse and Add! operation carried out in base 2, written in base 10. |
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+0
2
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| 537, 1146, 1899, 3618, 4713, 9522, 14427, 28386, 37533, 84966, 138123, 353004, 466209, 738024, 833301, 1525224, 1718853, 3048912, 3239469, 6196176, 6583437, 12389280, 12770397, 24975264, 25749789, 49944384, 50706621, 100282176
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The base 2 trajectory of 537 = A075252(3) provably does not contain a palindrome. 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. - The generating function given describes the sequence from a(12) onward; the g.f. for the complete sequence is known but nearly twice as big.
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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), ..., a(11) as above; for n >11 and n = 0 (mod 4): a(n) = 3*2^(2*k+13)+18249*2^k-3 where k = (n-4)/4; n = 1 (mod 4): a(n) = 6*2^(2*k+13)-12102*2^k where k = (n-5)/4; n = 2 (mod 4): a(n) = 6*2^(2*k+13)+11718*2^k-3 where k = (n-6)/4; n = 3 (mod 4): a(n) = 12*2^(2*k+13)-11910*2^k where k = (n-7)/4. G.f.: -3*(492528*x^7+293388*x^6-508920*x^5-260350*x^4-229616*x^3-188442*x^2+246008*x+155403)/ ((x-1)*(x+1)*(2*x^2-1)*(2*x^4-1))
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EXAMPLE
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537 (decimal) = 1000011001 -> 1000011001 + 1001100001 = 10001111010= 1146 (decimal).
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PROGRAM
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(PARI) {m=537; stop=30; 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. A075252, A061561, A075253, A075268, A077077.
Sequence in context: A165989 A067723 A059949 this_sequence A033916 A111258 A118630
Adjacent sequences: A077073 A077074 A077075 this_sequence A077077 A077078 A077079
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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), Oct 25 2002
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