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

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

Offset: 1

Author

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

Keywords

• nonn
• base
• less

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).

Examples

			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
		

Links

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

Crossrefs

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

Formula

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