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A048715 Binary expansion matches (100(0)*)*; or, Zeckendorf-like expansion of n using recurrence f(n) = f(n-1) + f(n-3). 12
0, 1, 2, 4, 8, 9, 16, 17, 18, 32, 33, 34, 36, 64, 65, 66, 68, 72, 73, 128, 129, 130, 132, 136, 137, 144, 145, 146, 256, 257, 258, 260, 264, 265, 272, 273, 274, 288, 289, 290, 292, 512, 513, 514, 516, 520, 521, 528, 529, 530, 544, 545, 546, 548, 576, 577, 578, 580 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

No more than one 1-bit in each bit triplet. All terms satisfy A048727(n) = 7*n.

Constructed from A000930 in the same way as A003714 is constructed from A000045.

It appears that n is in the sequence if and only if C(7n,n) is odd (cf. A003714). - Benoit Cloitre, Mar 09 2003

The conjecture by Benoit is correct. This is easily proved using the well-known result that the multiplicity with which a prime p divides C(n+m,n) is the number of carries when adding n+m in base p. - Franklin T. Adams-Watters, Oct 06 2009

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1275

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

Index entries for 2-automatic sequences.

FORMULA

a(0) = 0, a(n) = (2^(invfoo(n)-1))+a(n-foo(invfoo(n))), where foo(n) is foo(n-1) + foo(n-3) (A000930) and invfoo is its "integral" (floored down) inverse.

a(n) XOR 6*a(n) = 7*a(n); 3*a(n) XOR 4*a(n) = 7*a(n); 3*a(n) XOR 5*a(n) = 6*a(n); (conjectures). - Paul D. Hanna, Jan 22 2006

MATHEMATICA

Reap[Do[If[OddQ[Binomial[7n, n]], Sow[n]], {n, 0, 400}]][[2, 1]]

PROG

(PARI) is(n)=!bitand(n, 6*n) \\ Charles R Greathouse IV, Oct 03 2016

CROSSREFS

Subsequence of A048716.

Cf. A048717-A048719, A004742-A004744, A003726, A048730, A048733, A115422-A115424.

Sequence in context: A182653 A036349 A155562 * A242662 A028982 A175338

Adjacent sequences:  A048712 A048713 A048714 * A048716 A048717 A048718

KEYWORD

nonn,easy

AUTHOR

Antti Karttunen, Mar 30 1999

STATUS

approved

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Last modified May 24 22:11 EDT 2017. Contains 287008 sequences.