A181483 Number of powers of 2 which can be subtracted from 3^n to form primes

1, 2, 3, 3, 5, 2, 4, 3, 4, 3, 5, 1, 3, 2, 3, 4, 4, 1, 5, 2, 6, 4, 2, 1, 4, 1, 5, 2, 8, 1, 6, 1, 5, 3, 7, 0, 6, 3, 1, 0, 9, 1, 8, 8, 5, 1, 4, 4, 6, 1, 6, 1, 4, 3, 5, 3, 2, 2, 4, 2, 2, 3, 3, 5, 2, 0, 7, 1, 5, 2, 3, 4, 5, 2, 1, 4, 5, 1, 4, 1, 4, 5, 4, 3, 4, 2, 6, 1, 9, 3, 3, 2, 2, 2, 5, 2, 3, 1, 5, 1, 6, 3, 1, 5, 4

Offset

1,2

Comments

Note that if a 2^m is too large or too small, 3^n-2^m is either negative or fractional (respectively) and cannot ever be prime, thus 0 <= a(n) <= floor(n*log_2(3))

Zeros in this sequence are in A181484, which correspond to -1s in A180303

Links

Table of n, a(n) for n=1..105.

Example

3^1-2^0 = 2 which is prime, so a(1)=1
3^3-{2^4,2^3,2^2,2^1,2^0} = {11,19,23,25,26}, three of which are prime, so a(3) = 3

Mathematica

np[n_]:=Module[{p2=2^Range[0, Floor[Log[2, 3^n]]]}, Count[3^n-p2, _?PrimeQ]]; Array[np, 110] (* Harvey P. Dale, Nov 06 2012 *)

Crossrefs

Cf. A013604, A014224, A180303, A181484

Sequence in context: A341931 A341701 A049272 * A205130 A324799 A069461

Adjacent sequences: A181480 A181481 A181482 * A181484 A181485 A181486

Keyword

nonn

Author

Carl R. White, Oct 23 2010

Status

approved