A284267 - OEIS

%I #15 Mar 28 2017 14:53:11

%S 1,2,1,3,2,2,1,4,3,1,1,2,2,2,1,5,4,1,2,1,1,2,1,2,2,1,1,2,2,2,1,6,5,1,

%T 2,2,2,1,1,1,1,1,1,2,2,2,1,2,2,1,2,1,1,2,1,2,2,1,1,2,2,2,1,7,6,1,2,2,

%U 2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,2,1,2,2,1,1,2,2,2,1,2,2,1,2,2,2,1,1,1,1,1,1,2,2,2,1,2,2,1,2,1,1,2,1,2,2

%N Number of terms with coefficient 1 in the Stern polynomial B(2n+1,x): a(n) = A056169(A277324(n))

%C Number of 1's on row 2n+1 of table A125184.

%H Antti Karttunen, <a href="/A284267/b284267.txt">Table of n, a(n) for n = 0..8192</a>

%F a(n) = A284271((2*n)+1).

%F a(n) = A056169(A277324(n)).

%F Other identities. For all n >= 0:

%F A007306(1+n) = a(n) + A284268(n).

%t A003961[p_?PrimeQ] := A003961[p] = Prime[ PrimePi[p] + 1]; A003961[1] = 1; A003961[n_]:= A003961[n] = Times @@ (A003961[First[#]] ^ Last[#] & ) /@ FactorInteger[n] (* after _Jean-François Alcover_, Dec 01 2011 *); A260443[n_]:= If[n<2, n + 1, If[EvenQ[n], A003961[A260443[n/2]], A260443[(n - 1)/2] * A260443[(n + 1)/2]]]; a[n_]:= If[n<2, 0, Count[Transpose[FactorInteger[n]][[2]], 1]]; A277324[n_]:=A260443[2n + 1]; Table[a[A277324[n]], {n, 0, 150}] (* _Indranil Ghosh_, Mar 28 2017 *)

%o (PARI) A284267(n) = A284271(n+n+1); \\ Other code as in A284271.

%o (Scheme)

%o (define (A284267 n) (A284271 (+ n n 1)))

%o (define (A284267 n) (A056169 (A277324 n)))

%Y Cf. A007306, A056169, A125184, A260443, A277324, A284268.

%Y Odd bisection of A284271.

%K nonn

%O 0,2

%A _Antti Karttunen_, Mar 25 2017