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A048716 Numbers n such that binary expansion matches ((0)*00(1?)1)*(0*). 9
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 (list; graph; refs; listen; history; text; internal format)
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 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." - Jason Kimberley, Dec 21 2011

A116361(a(n)) <= 2. - Reinhard Zumkeller, Feb 04 2006

LINKS

Table of n, a(n) for n=1..63.

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]]

PROG

(PARI) is(n)=!bitand(n, n>>2) \\ Charles R Greathouse IV, Oct 03 2016

CROSSREFS

Superset of A048715 and A048719. 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,easy

AUTHOR

Antti Karttunen, 30.3.1999

STATUS

approved

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Last modified November 20 10:31 EST 2017. Contains 294963 sequences.