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

%I

%S 9,17,65,257,4097,16385,262145,1048577,16777217,1073741825,4294967297,

%T 274877906945,4398046511105,17592186044417,281474976710657,

%U 18014398509481985,1152921504606846977,4611686018427387905,295147905179352825857,4722366482869645213697

%N a(n) = 2^(prime(n) + 1) + 1.

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

%e prime(n)=a ==> convert(1 (0xa times) 1,decimal,2) = b # note a zeros

%e ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

%e prime(1)=2 ==> convert(1001,decimal,2) = 9 # note 2 zeros

%e prime(2)=3 ==> convert(10001,decimal,2) = 17 # note 3 zeros

%e prime(3)=5 ==> convert(1000001,decimal,2) = 65 # note 5 zeros

%e prime(3)=7 ==> convert(100000001,decimal,2) = 257 # note 7 zeros

%p 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);

%t Table[2^(Prime[n] + 1) + 1, {n, 18}] (* _Robert G. Wilson v_, Dec 22 2004 *)

%o (MAGMA) [2^(NthPrime(n)+1)+1: n in [1..20]]; // _Vincenzo Librandi_, Jul 30 2015

%Y Cf. A000051.

%K nonn

%O 1,1

%A _Jorge Coveiro_, Dec 22 2004

%E Edited and extended by _Robert G. Wilson v_, Dec 22 2004

%E a(19)-a(20) from _Vincenzo Librandi_, Jul 30 2015

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Last modified February 21 05:23 EST 2020. Contains 332086 sequences. (Running on oeis4.)