A101304 a(n) = 2^(prime(n) + 1) + 1.

9, 17, 65, 257, 4097, 16385, 262145, 1048577, 16777217, 1073741825, 4294967297, 274877906945, 4398046511105, 17592186044417, 281474976710657, 18014398509481985, 1152921504606846977, 4611686018427387905, 295147905179352825857, 4722366482869645213697

Offset: 1

Author

Jorge Coveiro, Dec 22 2004

Keywords

• nonn

Comments

Decimal numbers in which binary form is given by 1x1 where x is the digit 0 repeated a prime number of times.

Examples

			prime(n)=a ==> convert(1 (0xa times) 1,decimal,2) = b # note a zeros
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
prime(1)=2 ==> convert(1001,decimal,2) = 9 # note 2 zeros
prime(2)=3 ==> convert(10001,decimal,2) = 17 # note 3 zeros
prime(3)=5 ==> convert(1000001,decimal,2) = 65 # note 5 zeros
prime(3)=7 ==> convert(100000001,decimal,2) = 257 # note 7 zeros
		

Crossrefs

Cf. A000051.

Programs

Magma

[2^(NthPrime(n)+1)+1: n in [1..20]]; // Vincenzo Librandi, Jul 30 2015

Maple

convert(1001, decimal, 2), convert(10001, decimal, 2), convert(1000001, decimal, 2), convert(100000001, decimal, 2), convert(1000000000001, decimal, 2), convert(100000000000001, decimal, 2), convert(1000000000000000001, decimal, 2), convert(100000000000000000001, decimal, 2), convert(1000000000000000000000001, decimal, 2), convert(1000000000000000000000000000001, decimal, 2), convert(100000000000000000000000000000001, decimal, 2);

Mathematica

Table[2^(Prime[n] + 1) + 1, {n, 18}] (* Robert G. Wilson v, Dec 22 2004 *)

Extensions

Edited and extended by Robert G. Wilson v, Dec 22 2004

a(19)-a(20) from Vincenzo Librandi, Jul 30 2015