A093052 Exponent of 2 in 6^n - 2^n.

0, 2, 5, 4, 8, 6, 9, 8, 13, 10, 13, 12, 16, 14, 17, 16, 22, 18, 21, 20, 24, 22, 25, 24, 29, 26, 29, 28, 32, 30, 33, 32, 39, 34, 37, 36, 40, 38, 41, 40, 45, 42, 45, 44, 48, 46, 49, 48, 54, 50, 53, 52, 56, 54, 57, 56, 61, 58, 61, 60, 64, 62, 65, 64, 72, 66, 69, 68, 72

Offset: 0

Author

Ralf Stephan, Mar 16 2004

Keywords

• nonn

Crossrefs

a(n-1) is the exponent of 2 in A009168(n), A012394(n), A088991(n), A009083(n), A012036(n), A012092(n), A012395(n), A012460(n), A012465(n), A012466(n), A012467(n), (A049294(n)-1)/3.

Cf. A093050, A093051.

Programs

Mathematica

Join[{0},Table[IntegerExponent[6^n-2^n,2],{n,70}]] (* Harvey P. Dale, Mar 08 2012 *)

PARI

a(n)=if(n<1,0,if(n%2==0,a(n/2)+2*floor((n+2)/4)+1,n+1))

Python

def A093052(n): return n+(~(m:=3**n-1)& m-1).bit_length() if n else 0 # Chai Wah Wu, Jul 07 2022

Formula

Recurrence: a(2n) = a(n) + [(n+1)/2] + 1, a(2n+1) = 2n+2.

a(n) = n + A007814(A024023(n)) = n + A090740(n). - Reinhard Zumkeller, Mar 27 2004