

A048715


Binary expansion matches (100(0)*)*; or, Zeckendorflike expansion of n using recurrence f(n) = f(n1) + f(n3).


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
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OFFSET

0,3


COMMENTS

No more than one 1bit in each bit triple. 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 wellknown 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. AdamsWatters, 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 2automatic sequences.


FORMULA

a(0) = 0, a(n) = (2^(invfoo(n)1))+a(nfoo(invfoo(n))), where foo(n) is foo(n1) + foo(n3) (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]]
(* Second program: *)
filterQ[n_] := With[{bb = IntegerDigits[n, 2]}, !MatchQ[bb, {___, 1, 0, 1, ___}{___, 1, 1, ___}]];
Select[Range[0, 580], filterQ] (* JeanFrançois Alcover, Dec 31 2020 *)


PROG

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


CROSSREFS

Subsequence of A048716.
Cf. A048717A048719, A004742A004744, A003726, A048730, A048733, A115422A115424.
Sequence in context: A182653 A036349 A155562 * A336232 A242662 A335851
Adjacent sequences: A048712 A048713 A048714 * A048716 A048717 A048718


KEYWORD

nonn,base,easy


AUTHOR

Antti Karttunen, Mar 30 1999


STATUS

approved



