A181484 -id:A181484 - cp's OEIS frontend

A180303 a(n) = smallest number such that 3^n-2^a(n) is prime, or -1 if no such number exists.

0, 1, 2, 1, 1, 1, 3, 3, 1, 7, 4, 11, 6, 3, 4, 9, 9, 5, 6, 3, 2, 1, 7, 35, 12, 29, 10, 13, 6, 11, 2, 21, 8, 27, 11, -1, 1, 17, 10, -1, 1, 37, 8, 9, 16, 61, 23, 23, 17, 27, 4, 7, 2, 7, 7, 39, 58, 81, 30, 17, 60, 3, 8, 13, 18, -1, 20, 101, 4, 73, 27, 17, 2, 17, 19, 13, 41, 53, 44, 111, 34, 13

Offset: 1

Carl R. White, Aug 25 2010

sign

From Carl R. White, Oct 23 2010: (Start)
Entries where a(n) = 1 can be found in A014224.
Entries where a(n) = -1 can be found in A181484. (End)

			3^1-2^0 = 2, so a(1)=0; no other terms are zero.
3^11-2^1, 3^11-2^2, 3^11-2^3 are all nonprime, but 3^11-2^4 = 177131 which is prime so a(11) = 4.
a(36) is -1 (the placeholder value) because nonprimes are obtained when any power of two is subtracted from 3^36.

Cf. A013604.

Cf. A014224, A181483, A181484. - Carl R. White, Oct 23 2010

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

Original entry on oeis.org

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

Carl R. White, Oct 23 2010

nonn

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

			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

Cf. A013604, A014224, A180303, A181484

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 *)

cp's OEIS Frontend

A180303 a(n) = smallest number such that 3^n-2^a(n) is prime, or -1 if no such number exists.

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