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A048716 Numbers n such that binary expansion matches ((0)*00(1?)1)*(0*). 9

%I

%S 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,

%T 64,65,66,67,68,70,72,73,76,96,97,98,99,100,102,128,129,130,131,132,

%U 134,136,137,140,144,145,146,147,152,153,192,193,194,195,196,198,200,201

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

%C If bit i is 1, then bits i+-2 must be 0. All terms satisfy A048725(n) = 5*n.

%C It appears that n is in the sequence if and only if C(5n,n) is odd (cf. A003714). - _Benoit Cloitre_, Mar 09 2003

%C 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

%C A116361(a(n)) <= 2. - _Reinhard Zumkeller_, Feb 04 2006

%H <a href="/index/Con#CongruCrossDomain">Index entries for sequences defined by congruent products between domains N and GF(2)[X]</a>

%H <a href="/index/Con#CongruXOR">Index entries for sequences defined by congruent products under XOR</a>

%t Reap[Do[If[OddQ[Binomial[5n, n]], Sow[n]], {n, 0, 400}]][[2, 1]]

%o (PARI) is(n)=!bitand(n,n>>2) \\ _Charles R Greathouse IV_, Oct 03 2016

%Y Superset of A048715 and A048719. Cf. A048729, A003714, A115845, A115847, A116360.

%K nonn,easy

%O 1,3

%A Antti Karttunen, 30.3.1999

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Last modified June 17 17:12 EDT 2019. Contains 324196 sequences. (Running on oeis4.)