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A048718 Binary expansion matches ((0)*0001)*(0*); or, Zeckendorf-like expansion of n using recurrence f(n) = f(n-1) + f(n-4). 7
0, 1, 2, 4, 8, 16, 17, 32, 33, 34, 64, 65, 66, 68, 128, 129, 130, 132, 136, 256, 257, 258, 260, 264, 272, 273, 512, 513, 514, 516, 520, 528, 529, 544, 545, 546, 1024, 1025, 1026, 1028, 1032, 1040, 1041, 1056, 1057 (list; graph; refs; listen; history; internal format)
OFFSET

0,3

COMMENTS

Max. 1 one-bit occur in each range of four bits.

Constructed from A003269 in the same way as A003714 is constructed from A000045.

LINKS

Index entries for sequences defined by congruent products between domains N and GF(2)[X]

Index entries for sequences defined by congruent products under XOR

FORMULA

a(0) = 0, a(n) = (2^(invfyy(n)-1))+a(n-fyy(invfyy(n))) where fyy(n) is fyy(n-1) + fyy(n-4) (A003269) and invfyy is its "integral" (floored down) inverse.

a(n) XOR 14*a(n) = 15*a(n); 3*a(n) XOR 9*a(n) = 10*a(n); 3*a(n) XOR 13*a(n) = 14*a(n); 5*a(n) XOR 9*a(n) = 12*a(n); 5*a(n) XOR 11*a(n) = 14*a(n); 6*a(n) XOR 11*a(n) = 13*a(n); 7*a(n) XOR 9*a(n) = 14*a(n); 7*a(n) XOR 10*a(n) = 13*a(n); 7*a(n) XOR 11*a(n) = 12*a(n); 12*a(n) XOR 21*a(n) = 25*a(n); 12*a(n) XOR 37*a(n) = 41*a(n); etc. (conjectures). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 22 2006

CROSSREFS

Cf. A048715, A048719, A115422, A115423, A115424.

Sequence in context: A061681 A100787 A115795 * A018510 A018366 A127066

Adjacent sequences:  A048715 A048716 A048717 * A048719 A048720 A048721

KEYWORD

nonn

AUTHOR

Antti Karttunen, 30.3.1999

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Last modified February 15 15:20 EST 2012. Contains 205823 sequences.