A180303 -id:A180303 - cp's OEIS frontend

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

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 *)

A181484 Numbers k such that no power of 2 can be subtracted from 3^k to make a prime.

Original entry on oeis.org

36, 40, 66, 124, 162, 170, 179, 182, 184, 198, 206, 212, 214, 230, 262, 288, 302, 356, 358, 368, 393, 402, 406, 448, 456, 468, 493, 546, 586, 666, 676, 683, 686, 690, 702, 718, 724, 738, 752, 760, 785, 844, 854, 862, 866, 870, 882, 884, 888, 904, 918, 980

Offset: 1

Carl R. White, Oct 23 2010

nonn

Zeros of A181483, -1s of A180303.

Odd terms: 179, 393, 493, 683, 785, 1083, 1161, 1181, 1545, ..., . - Robert G. Wilson v, Oct 25 2010

Cf. A013604, A014224, A180303, A181483.

fQ[n_] := Block[{k = 0, lmt = Floor@ Log[2, 3^n] +1, m = 3^n}, While[ k < lmt && !PrimeQ[m - 2^k], k++ ]; k == lmt]; Select[ Range@ 995, fQ] (* Robert G. Wilson v, Oct 25 2010 *)

a(30) onwards from Robert G. Wilson v, Oct 25 2010

Name clarified by J. Lowell, Aug 21 2020

cp's OEIS Frontend

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

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