A117085 Decimal value of binary number whose n-th 1 is followed by L(n) 0's.

9, 37, 593, 18977, 4858113, 19898830849, 10432718228160513, 11202045899583117393395713, 3153095608696857509125380749498911817729, 476482336633392067336089761008918511215119000704844672205324289

Offset

1,1

Comments

This is to Lucas numbers as A117067 "Decimal value of binary number whose n-th 1 is followed by F(n) 0's" is to Fibonacci numbers. Primes include a(2) = 37 and a(3) = 593.

Links

Table of n, a(n) for n=1..10.

Formula

a(0) = 1, for positive n: a(n+1) = 1 + a(n)*2^(1+L(n)) = 1 + a(n)*2^(1+A000032(n)).

Example

a(1) = 9 because 1001 (base 2) = 1 + 2^(1+2) = 9 (base 10), where the two 0's correspond to L(0) = A000032(0) = 2.
a(2) = 37 because 100101 (base 2) = 1 + (1 + 2^(1+2))*2^(1+1) = 37 (base 10).
a(3) = 593 because 1001010001 (base 2) = 1 + (1 + (1 + 2^(1+2))*2^(1+1))*2^(1+3) = 593(base 10).

Mathematica

a[0] = 1; a[n_] := a[n] = 1 + a[n-1]*2^(1 + LucasL[n-1]); a /@ Range[10] (* Giovanni Resta, Jun 15 2016 *)

Crossrefs

Cf. A000032, A117011, A117067, A117068.

Sequence in context: A370269 A026686 A076174 * A120780 A071229 A071238

Adjacent sequences: A117082 A117083 A117084 * A117086 A117087 A117088

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Apr 17 2006

Status

approved