A101304 - OEIS

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

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OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

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

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 *)

PROG

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

CROSSREFS

Cf. A000051.

Sequence in context: A147138 A282764 A319018 * A146601 A121955 A151793

Adjacent sequences: A101301 A101302 A101303 * A101305 A101306 A101307

KEYWORD

nonn

AUTHOR

Jorge Coveiro, 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

STATUS

approved