A117067 Decimal value of binary number whose n-th 1 is followed by F(n) 0's.

1, 5, 21, 169, 2705, 173121, 88637953, 1452244221953, 6091153749114355713, 209290449178831574011566096385, 15080966222943833716372357571365139853460111361

Offset

0,2

Comments

a(1) = 5 is prime; a(6) = 88637953 is prime.

a(17) has 1264 digits, too large for a b-file. - Robert Israel, Jun 15 2016

Links

Robert Israel, Table of n, a(n) for n = 0..16

Formula

a(0) = 1 and a(n) = 1 + a(n-1) * 2^(1+F(n)) for n>0, where F(i) = A000045(i).

a(n+1) = 1 + a(n)*(a(n)-1)*(a(n-1)-1)/(2*a(n-1)*a(n-2)). - Robert Israel, Jun 15 2016

Example

a(1) = 5 because 101 (base 2) = 5 (base 10).
a(2) = 21 because 10101 (base 2) = 21 (base 10).
a(3) = 169 because 10101001 (base 2) = 169 (base 10).
a(4) = 2705 because 101010010001 (base 2) = 2705 (base 10).
a(5) = 173121 because 101010010001000001 (base 2) = 173121 (base 10).

Maple

f:= proc(n) option remember; procname(n-1)*(procname(n-1)-1)*(procname(n-2)-1)/(2*procname(n-2)*procname(n-3))+1 end proc;
f(0):= 1: f(1):= 5: f(2):= 21:
map(f, [$0..15]); # Robert Israel, Jun 15 2016

Mathematica

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

Prog

(Magma) I:=[1, 5, 21]; [n le 3 select I[n] else 1+Self(n-1)*(Self(n-1)-1)*(Self(n-2)-1)/(2*Self(n-2)*Self(n-3)): n in [1..12]]; // Vincenzo Librandi, Jun 16 2016

Crossrefs

Cf. A000040, A000045.

Sequence in context: A284231 A182825 A318966 * A123334 A140196 A027160

Adjacent sequences: A117064 A117065 A117066 * A117068 A117069 A117070

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Apr 16 2006

Extensions

a(0) added and formula corrected by Giovanni Resta, Jun 15 2016

Status

approved