

A048716


Numbers n such that binary expansion matches ((0)*00(1?)1)*(0*).


13



0, 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 19, 24, 25, 32, 33, 34, 35, 36, 38, 48, 49, 50, 51, 64, 65, 66, 67, 68, 70, 72, 73, 76, 96, 97, 98, 99, 100, 102, 128, 129, 130, 131, 132, 134, 136, 137, 140, 144, 145, 146, 147, 152, 153, 192, 193, 194, 195, 196, 198, 200, 201
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OFFSET

1,3


COMMENTS

If bit i is 1, then bits i+2 must be 0. All terms satisfy A048725(n) = 5*n.
It appears that n is in the sequence if and only if C(5n,n) is odd (cf. A003714).  Benoit Cloitre, Mar 09 2003
Yes, as remarked in A048715, "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."  Jason Kimberley, Dec 21 2011
A116361(a(n)) <= 2.  Reinhard Zumkeller, Feb 04 2006


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for 2automatic sequences.
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


MATHEMATICA

Reap[Do[If[OddQ[Binomial[5n, n]], Sow[n]], {n, 0, 400}]][[2, 1]]
(* Second program: *)
filterQ[n_] := With[{bb = IntegerDigits[n, 2]}, MatchQ[bb, {0}{1}{1, 1}{___, 0, _, 1, ___}{___ 1, _, 0, ___}] && !MatchQ[bb, {___, 1, _, 1, ___}]];
Select[Range[0, 201], filterQ] (* JeanFrançois Alcover, Dec 31 2020 *)


PROG

(PARI) is(n)=!bitand(n, n>>2) \\ Charles R Greathouse IV, Oct 03 2016
(PARI) list(lim)=my(v=List(), n, t); while(n<=lim, t=bitand(n, n>>2); if(t, n+=1<<valuation(t, 2), listput(v, n); n++)); Vec(v) \\ Charles R Greathouse IV, Oct 22 2021


CROSSREFS

Superset of A048715 and A048719. Union of A004742 and A003726.
Cf. A048729, A003714, A115845, A115847, A116360.
Sequence in context: A002348 A019469 A081491 * A010434 A074230 A064438
Adjacent sequences: A048713 A048714 A048715 * A048717 A048718 A048719


KEYWORD

nonn,base,easy


AUTHOR

Antti Karttunen, Mar 30 1999


STATUS

approved



