A111209 - OEIS

%I #19 Sep 08 2022 08:45:20

%S 0,1,3,9,21,51,111,237,489,995,2017,4059,8151,16341,32721,65483,

%T 131013,262083,524221,1048505,2097079,4194225,8388525,16777127,

%U 33554335,67108763,134217625,268435349,536870803,1073741711,2147483521,4294967165,8589934455,17179869045

%N Difference between the powers of two and the primes.

%C 2*a(n) < a(n+1) because 2*prime(n) > prime(n+1) (see A062234). We have a(n) - a(1) < a(n+1) - a(n) so this is a B_2 sequence. - _Thomas Ordowski_, Sep 23 2014

%F a(n) = 2^n - prime(n).

%F a(n) = A000079(n) - A000040(n). - _Wesley Ivan Hurt_, Sep 23 2014

%p A111209:=n->2^n-ithprime(n): seq(A111209(n), n=1..30); # _Wesley Ivan Hurt_, Sep 23 2014

%t Table[2^n - Prime[n], {n, 25}]

%o (PARI) vector(50, n, 2^n - prime(n)) \\ _Michel Marcus_, Sep 23 2014

%o (Magma) [2^n-NthPrime(n) : n in [1..30]]; // _Wesley Ivan Hurt_, Sep 23 2014

%Y Cf. A000040, A000079.

%K nonn,easy

%O 1,3

%A _Roger L. Bagula_, Oct 25 2005

%E More terms from _Michel Marcus_, Sep 23 2014