A138831 n-th perfect number minus 1, written in base 2.

101, 11011, 111101111, 1111110111111, 1111111111110111111111111, 111111111111111101111111111111111, 1111111111111111110111111111111111111

Offset

1,1

Comments

Subset of A138148, cyclops numbers with binary digits, only.

Subset of A002113, palindromes in base 10.

a(n) has 2*A090748(n) digits 1.

The number of digits of a(n) is 2*A000043(n)-1, equal to A133033(n), the number of proper divisors of n-th perfect number.

a(n) = (A135627(n) written in base 2).

Links

Table of n, a(n) for n=1..7.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Formula

a(n) = A138148(A090748(n)).

Example

n ... A000396(n) - 1 = A135627(n) ............. a(n)
1 ............ 6 - 1 = ...... 5 ............... 101
2 ........... 28 - 1 = ..... 27 .............. 11011
3 .......... 496 - 1 = .... 495 ............ 111101111
4 ......... 8128 - 1 = ... 8127 .......... 1111110111111
5 ..... 33550336 - 1 = 33550335 .... 1111111111110111111111111

Crossrefs

Cf. A000043, A000396, A090748, A133033, A134808, A135627, A138131, A138148.

Sequence in context: A083981 A267779 A138148 * A267920 A300570 A171825

Adjacent sequences: A138828 A138829 A138830 * A138832 A138833 A138834

Keyword

nonn,base,less

Author

Omar E. Pol, Apr 08 2008, Apr 09 2008, Apr 14 2008

Status

approved