A085431 a(n) = (2^(n-1) + prime(n+1)-prime(n))/2.

1, 2, 3, 6, 9, 18, 33, 66, 131, 257, 515, 1026, 2049, 4098, 8195, 16387, 32769, 65539, 131074, 262145, 524291, 1048578, 2097155, 4194308, 8388610, 16777217, 33554434, 67108865, 134217730, 268435463, 536870914, 1073741827, 2147483649

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

( (1, 2, 4, 8, 16...) + (1, 2, 2, 4, 2...) ) / 2.

Maple

A085431:=n->(2^(n-1)+ithprime(n+1)-ithprime(n))/2: seq(A085431(n), n=1..50); # Wesley Ivan Hurt, Apr 11 2017

Mathematica

f[n_] := 2^(n - 2) + (Prime[n + 1] - Prime[n])/2; Table[ f[n], {n, 1, 34}]

Prog

(Magma) [(2^(n-1)+NthPrime(n+1)-NthPrime(n))/2: n in [1..40]]; // Vincenzo Librandi, Apr 12 2017

Crossrefs

Cf. A000079, A001223.

Sequence in context: A018518 A091326 A113863 * A108862 A298413 A268610

Adjacent sequences: A085428 A085429 A085430 * A085432 A085433 A085434

Keyword

nonn,easy

Author

David G. Williams (Davwill24(AT)aol.com), Aug 13 2003

Extensions

Edited and extended by Robert G. Wilson v and Ray Chandler, Aug 15 2003

Status

approved