cp's OEIS Frontend

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

%I A101304 #14 Sep 08 2022 08:45:16
%S A101304 9,17,65,257,4097,16385,262145,1048577,16777217,1073741825,4294967297,
%T A101304 274877906945,4398046511105,17592186044417,281474976710657,
%U A101304 18014398509481985,1152921504606846977,4611686018427387905,295147905179352825857,4722366482869645213697
%N A101304 a(n) = 2^(prime(n) + 1) + 1.
%C A101304 Decimal numbers in which binary form is given by 1x1 where x is the digit 0 repeated a prime number of times.
%e A101304 prime(n)=a ==> convert(1 (0xa times) 1,decimal,2) = b # note a zeros
%e A101304 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
%e A101304 prime(1)=2 ==> convert(1001,decimal,2) = 9 # note 2 zeros
%e A101304 prime(2)=3 ==> convert(10001,decimal,2) = 17 # note 3 zeros
%e A101304 prime(3)=5 ==> convert(1000001,decimal,2) = 65 # note 5 zeros
%e A101304 prime(3)=7 ==> convert(100000001,decimal,2) = 257 # note 7 zeros
%p A101304 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 A101304 Table[2^(Prime[n] + 1) + 1, {n, 18}] (* _Robert G. Wilson v_, Dec 22 2004 *)
%o A101304 (Magma) [2^(NthPrime(n)+1)+1: n in [1..20]]; // _Vincenzo Librandi_, Jul 30 2015
%Y A101304 Cf. A000051.
%K A101304 nonn
%O A101304 1,1
%A A101304 _Jorge Coveiro_, Dec 22 2004
%E A101304 Edited and extended by _Robert G. Wilson v_, Dec 22 2004
%E A101304 a(19)-a(20) from _Vincenzo Librandi_, Jul 30 2015