cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 23 2011

Keywords

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

Examples

			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

Links

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.

Programs

  • 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 ]]

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

Original entry on oeis.org

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

Views

Author

Max Alekseyev, Nov 24 2010

Keywords

Comments

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

Links

Crossrefs

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

Extensions

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

Views

Author

Clark Kimberling, Jul 30 2023

Keywords

Examples

			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,... .

Crossrefs

Complement of A007643.
Cf. A000040, A000079, A000244, A014121, A321671, A363999, A364000.

Programs

  • Mathematica
    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 *)

A323698 Primes of the form 3^j - 2^k, for j>=0, k>=0.

Original entry on oeis.org

2, 5, 7, 11, 17, 19, 23, 73, 79, 139, 179, 211, 227, 239, 241, 601, 727, 1163, 1931, 2179, 3299, 4513, 6529, 6553, 11491, 19427, 19681, 50857, 58537, 58921, 111611, 144379, 176123, 177019, 177131, 529393, 545747, 1593299, 1594259, 2685817, 4782961, 9492289, 14346859
Offset: 1

Views

Author

Jinyuan Wang, Jan 24 2019

Keywords

Comments

In this sequence, only 5 and 17 make both j and k even numbers.
Generally, the way to prove that a number is not in this sequence is to successively take residues modulo 3, 8, 5, and 16 on both sides of the equation 3^j - 2^k = x.

Examples

			11 = 3^3 - 2^4, so 11 is a term.
41 == 1 (mod 8), 41 == 2 (mod 3), so j = 2*l, k = 2*m. 41 == 1 (mod 5), but 3^(2*l) - 2^(2*m) mod 5 is 0, 2 or 3. So 41 is not in this sequence.

Crossrefs

Cf. A000040, A192111.
Cf. A007643 (Primes not of form |3^x - 2^y|).
Cf. A321671 (Primes of the form 2^j - 3^k).

Programs

  • Mathematica
    c = 3; d = 2; t[i_, j_] := c^i - d^j;
u = Table[If[PrimeQ[t[i, j]] == True, u = t[i, j]], {i, 0, 20}, {j, 0, i*Log[d, c]}];
v = Union[Flatten[u]]
  • PARI
    forprime(p=1, 1000, k=0; x=3; y=1; while(k

Formula

Intersection of A000040 and A192111.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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