A192170 -id:A192170

Search: a192170 -id:a192170

Displaying 1-3 of 3 results found.

page 1

A192110

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

+10
9

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

(list; graph; refs; listen; history; text; internal format)

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.

KEYWORD

nonn,fini

AUTHOR

Clark Kimberling, Jun 23 2011

STATUS

approved

A192112

Monotonic ordering of nonnegative differences 2^i-4^j, for 40>=i>=0, j>=0.

+10
3

0, 1, 3, 4, 7, 12, 15, 16, 28, 31, 48, 60, 63, 64, 112, 124, 127, 192, 240, 252, 255, 256, 448, 496, 508, 511, 768, 960, 1008, 1020, 1023, 1024, 1792, 1984, 2032, 2044, 2047, 3072, 3840, 4032, 4080, 4092, 4095, 4096, 7168, 7936, 8128, 8176, 8188, 8191, 12288

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..51.

MATHEMATICA

c = 2; d = 4; 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. A192113.

The definitions of all 50 sequences starting with this one now state explicitly that it is assumed that i <= 40. This refers to A192112 A192113 A192114 A192115 A192116 A192117 A192118 A192119 A192120 A192121 A192122 A192123 A192124 A192125 A192147 A192148 A192149 A192150 A192151 A192152 A192153 A192154 A192155 A192156 A192157 A192158 A192159 A192160 A192161 A192162 A192163 A192164 A192165 A192166 A192167 A192168 A192169 A192170 A192171 A192172 A192193 A192194 A192195 A192196 A192197 A192198 A192199 A192200 A192201 A192202. - N. J. A. Sloane, Oct 21 2019

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 23 2011

STATUS

approved

A192169

Monotonic ordering of nonnegative differences 4^i-9^j, for 40>= i>=0, j>=0.

+10
3

0, 3, 7, 15, 55, 63, 175, 247, 255, 295, 943, 1015, 1023, 3367, 4015, 4087, 4095, 6487, 9823, 15655, 16303, 16375, 16383, 58975, 64807, 65455, 65527, 65535, 203095, 255583, 261415, 262063, 262135, 262143, 517135, 989527, 1042015, 1047847, 1048495, 1048567

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..40.

MATHEMATICA

c = 4; d = 9; 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. A192170.

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 24 2011

STATUS

approved

page 1

Search completed in 0.007 seconds