A014121 -id:A014121 - cp's OEIS frontend

A173671 Positive integers that cannot be expressed as 3^m-2^n where m and n are integers.

3, 4, 6, 9, 10, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100

Offset: 1

Max Alekseyev, Nov 24 2010

nonn

The complement of this set, i.e., integers of the form 3^m-2^n, is A192111. - M. F. Hasler, Nov 24 2010

H. Gauchman and I. Rosenholtz (Proposers), R. Martin (Solver), Difference of prime powers, Problem 1404, Math. Mag., 65 (No. 4, 1992), 265; Solution, Math. Mag., 66 (No. 4, 1993), 269.
Math Overflow, 3^n - 2^m = +-41 is not possible. How to prove it?, Several contributors, Jun 29 2010.

Cf. A075824, A074981, A014121, A192110, A192111, A227048, A321671.

Deleted unwarranted programs and b-file. - N. J. A. Sloane, Oct 21 2019

A363998 Primes of the form |2^i - 3^j|, for i >= 0, j >= 0.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 47, 61, 73, 79, 101, 127, 139, 179, 211, 227, 229, 239, 241, 269, 431, 503, 509, 601, 727, 997, 1021, 1163, 1319, 1931, 2039, 2179, 3299, 3853, 4093, 4513, 6529, 6553, 7949, 8111, 8191, 11491, 14197, 16141, 16381

Offset: 1

Clark Kimberling, Jul 30 2023

nonn

			As in A014121, numbers of the form |2^i - 3^j|, for i >=0, j>=0 are 0,1,2,3,5,7,8,11,..., in which the primes are 2,3,5,7,11,... .

Complement of A007643.

Cf. A000040, A000079, A000244, A014121, A321671, A363999, A364000.

z = 500;
t = Table[Abs[2^i - 3^j], {i, 0, z}, {j, 0, z}];
v = Union[Sort[Flatten[t]]]; (* A014121*)
Intersection[v, Prime[Range[200000]]]   (* A363998 *)

A128760 Number of ways to write n as the absolute difference of a power of 2 and a power of 3.

Original entry on oeis.org

1, 4, 1, 1, 0, 3, 0, 3, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0

Offset: 0

Reinhard Zumkeller, Mar 25 2007

nonn

a(A014121(n)) > 0; the only even numbers m with a(m)>0 are of the form m=3^k-1: a(A024023(n)) > 0;

Conjecture: there exists c>=23 such that a(n)<2 for n>c.

			a(1) = #{2^1 - 3^0, 2^2 - 3^1, 3^1 - 2^1, 3^2 - 2^3} = 4;
a(2) = #{3^1 - 2^0} = 1;
a(3) = #{2^2 - 3^0} = 1;
a(5) = #{2^3 - 3^1, 2^5 - 3^3, 3^2 - 2^2} = 3;
a(7) = #{2^3 - 3^0, 2^4 - 3^2, 3^2 - 2^1} = 3;
a(8) = #{3^2 - 2^0} = 1;
a(11) = #{3^3 - 2^4} = 1;
a(13) = #{2^4 - 3^1, 2^8 - 3^5} = 2;
a(15) = #{2^4 - 2^0} = 1;
a(17) = #{3^4 - 2^6} = 1;
a(19) = #{3^3 - 2^3} = 1;
a(23) = #{2^5 - 3^2, 3^3 - 2^2} = 2;
a(25) = #{3^3 - 2^1} = 1.

Max Alekseyev, Table of n, a(n) for n = 0..1000

Cf. A000079, A000244.

A363999 Numbers of the form |2^i - 3^j|, for i >= 1, j >= 1.

Original entry on oeis.org

1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 37, 47, 49, 55, 61, 65, 73, 77, 79, 101, 115, 119, 125, 139, 175, 179, 211, 217, 227, 229, 235, 239, 241, 247, 253, 269, 295, 431, 473, 485, 503, 509, 601, 665, 697, 713, 721, 725, 727, 781, 943, 997, 1015, 1021, 1163

Offset: 1

Clark Kimberling, Jul 30 2023

nonn

Cf. A014121, A363998, A364000, A364001.

A364001 Primes of the form |2^i - 3^j|, i >= 1, j >= 1.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 23, 29, 37, 47, 61, 73, 79, 101, 139, 179, 211, 227, 229, 239, 241, 269, 431, 503, 509, 601, 727, 997, 1021, 1163, 1319, 1931, 2039, 2179, 3299, 3853, 4093, 4513, 6529, 6553, 7949, 8111, 11491, 14197, 16141, 16381, 19427, 19681, 32687

Offset: 1

Clark Kimberling, Aug 09 2023

nonn

Cf. A014121, A192110, A192111, A363998.

z = 500;
t = Table[Abs[2^i - 3^j], {i, 1, z}, {j, 1, z}];
u = Sort[Flatten[t]];
v = Union[u] ; (* A363999 *)
w = (v - 1)/2 ;  (* A364000 *)
Intersection[v, Prime[Range[200000]]]  (* this sequence *)

A014122 Numbers of form |2^i +- 3^j|.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 17, 19, 23, 25, 26, 28, 29, 31, 33, 35, 37, 41, 43, 47, 49, 55, 59, 61, 63, 65, 67, 73, 77, 79, 80, 82, 83, 85, 89, 91, 97, 101, 113, 115, 119, 125, 127, 129, 131, 137, 139, 145, 155, 175, 179, 209, 211, 217, 227

Offset: 1

Richard C. Schroeppel

nonn

Based on checking i <= 100 and j <= 60.
Existing sequence correct for j <= 200000. - Sean A. Irvine, Oct 04 2018
2*k is a term iff 2*k = 3^j +- 1. - Sean A. Irvine, Oct 04 2018
Existing sequence correct for j <= 10^6. - David A. Corneth, Oct 04 2018
3*k is a term iff 3*k = 2^j +- 1. - Jon E. Schoenfield, Oct 04 2018

Cf. A014121, A056850.

Constraint on search moved from title to comments by Sean A. Irvine, Oct 04 2018

cp's OEIS Frontend

A173671 Positive integers that cannot be expressed as 3^m-2^n where m and n are integers.

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A363998 Primes of the form |2^i - 3^j|, for i >= 0, j >= 0.

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Mathematica

A128760 Number of ways to write n as the absolute difference of a power of 2 and a power of 3.

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A363999 Numbers of the form |2^i - 3^j|, for i >= 1, j >= 1.

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A364001 Primes of the form |2^i - 3^j|, i >= 1, j >= 1.

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A014122 Numbers of form |2^i +- 3^j|.

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