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

1,3

Comments

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

Links

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.

Example

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

Mathematica

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 ]]

Crossrefs

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.

Sequence in context: A097687 A032911 A157834 * A246026 A188574 A247458

Adjacent sequences: A192107 A192108 A192109 * A192111 A192112 A192113

Keyword

nonn,fini

Author

Clark Kimberling, Jun 23 2011

Status

approved