A173671 -id:A173671 - cp's OEIS frontend

A192110 Monotonic ordering of nonnegative differences 2^i - 3^j, for 40 >= i >= 0, j >= 0.

0, 1, 3, 5, 7, 13, 15, 23, 29, 31, 37, 47, 55, 61, 63, 101, 119, 125, 127, 175, 229, 247, 253, 255, 269, 295, 431, 485, 503, 509, 511, 781, 943, 997, 1015, 1021, 1023, 1319, 1631, 1805, 1909, 1967, 2021, 2039, 2045, 2047, 3367, 3853, 4015, 4069, 4087, 4093

Offset: 1

Clark Kimberling, Jun 23 2011

Comments from N. J. A. Sloane, Oct 21 2019: (Start)
Warning: Note the definition assumes i <= 40.
Because of this assumption, it is not true that this is (except for a(1)=0) the complement of A075824 in the odd integers.
However, by definition, it is the complement of A328077.
(End)
All 52 sequences in this set are finite. - Georg Fischer, Nov 16 2021

			The differences accrue like this:
1-1
2-1
4-3.....4-1
8-3.....8-1
16-9....16-3....16-1
32-27...32-9....32-3....32-1
64-27...64-9....64-3....64-1

Rok Cestnik, Table of n, a(n) for n = 1..534 [truncated to 2^40-1 by _Georg Fischer_, Nov 16 2021]
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, A173671, A192111, A328077 (complement).
For primes, see A007643, A007644, A321671.
This is the first of a set of 52 similar sequences:
A192110: 2^i-3^j, A192111: 3^i-2^j, A192112: 2^i-4^j, A192113: 4^i-2^j, A192114: 2^i-5^j, A192115: 5^i-2^j, A192116: 2^i-6^j, A192117: 6^i-2^j,
A192118: 2^i-7^j, A192119: 7^i-2^j, A192120: 2^i-8^j, A192121: 8^i-2^j, A192122: 2^i-9^j, A192123: 9^i-2^j, A192124: 2^i-10^j, A192125: 10^i-2^j,
A192147: 3^i-4^j, A192148: 4^i-3^j, A192149: 3^i-5^j, A192150: 5^i-3^j, A192151: 3^i-6^j, A192152: 6^i-3^j, A192153: 3^i-7^j, A192154: 7^i-3^j,
A192155: 3^i-8^j, A192156: 8^i-3^j, A192157: 3^i-9^j, A192158: 9^i-3^j, A192159: 3^i-10^j, A192160: 10^i-3^j, A192161: 4^i-5^j, A192162: 5^i-4^j,
A192163: 4^i-6^j, A192164: 6^i-4^j, A192165: 4^i-7^j, A192166: 7^i-4^j, A192167: 4^i-8^j, A192168: 8^i-4^j, A192169: 4^i-9^j, A192170: 9^i-4^j,
A192171: 4^i-10^j, A192172: 10^i-4^j, A192193: 5^i-6^j, A192194: 6^i-5^j, A192195: 5^i-7^j, A192196: 7^i-5^j, A192197: 5^i-8^j, A192198: 8^i-5^j,
A192199: 5^i-9^j, A192200: 9^i-5^j, A192201: 5^i-10^j, A192202: 10^i-5^j.

c = 2; d = 3; t[i_, j_] := c^i - d^j;
u = Table[t[i, j], {i, 0, 40}, {j, 0, i*Log[d, c]}];
v = Union[Flatten[u ]]

A192111 Monotonic ordering of nonnegative differences 3^i-2^j, for i>=0, j>=0.

Original entry on oeis.org

0, 1, 2, 5, 7, 8, 11, 17, 19, 23, 25, 26, 49, 65, 73, 77, 79, 80

Offset: 1

Clark Kimberling, Jun 23 2011

nonn

Complement of A173671 in the nonnegative integers.

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. A173671 (complement), A192110, A227048 (partial unions of rows).

Deleted unwarranted programs and b-file. Only the terms in A173671 (that is, up to 100) have been proved to be correct. - N. J. A. Sloane, Oct 21 2019

A328077 Complement of A192110.

Original entry on oeis.org

2, 4, 6, 8, 9, 10, 11, 12, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80

Offset: 1

N. J. A. Sloane, Oct 12 2019

nonn

Note that, because A192110 assumes i <= 40, it is incorrect to say that the present sequence consists of "the positive integers that cannot be expressed as 2^m-3^n where m and n are integers".

This sequence is included because one way to remove the assumption i <= 40 from A192110 (and the fifty other unproved sequences of the same type) would be to show that the complements are correct, using the method used to prove the correctness of A173671.

Math Overflow, 3^n - 2^m = +-41 is not possible. How to prove it?, Several contributors, Jun 29 2010.

Complement of A192110.

Cf. A192111, A173671.

Edited by N. J. A. Sloane, Oct 21 2019

A175832 Number of solutions of equation 3^q - 2^p = n over integer variables p, q.

Original entry on oeis.org

1, 2, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 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, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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

Offset: 0

Vladimir Reshetnikov, Sep 15 2010

nonn

a(n)=0 iff n is in A173671; a(n)>0 iff n is in A192111.

Edited and extended by Max Alekseyev, Jan 28 2012

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A192110 Monotonic ordering of nonnegative differences 2^i - 3^j, for 40 >= i >= 0, j >= 0.

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A192111 Monotonic ordering of nonnegative differences 3^i-2^j, for i>=0, j>=0.

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A328077 Complement of A192110.

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A175832 Number of solutions of equation 3^q - 2^p = n over integer variables p, q.

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