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.

Previous Showing 11-19 of 19 results.

A093680 Sequence contains no 3-term arithmetic progression, starting with 1, 19.

Original entry on oeis.org

1, 19, 20, 22, 23, 28, 29, 31, 32, 46, 47, 49, 50, 56, 58, 59, 82, 100, 101, 103, 104, 109, 110, 112, 113, 127, 128, 130, 131, 137, 139, 140, 244, 262, 263, 265, 266, 271, 272, 274, 275, 289, 290, 292, 293, 299, 301, 302, 325, 343, 344, 346, 347, 352, 353
Offset: 1

Views

Author

Ralf Stephan, Apr 09 2004

Keywords

Comments

a(1)=1, a(2)=19; a(n) is least k such that no three terms of a(1), a(2), ..., a(n-1), k form an arithmetic progression.

Links

Crossrefs

Cf. A004793, A033157, A093678, A093679, A093681, A092482.
Row 5 of array in A093682.

Formula

a(n) = (Sum_{k=1..n-1} (3^A007814(k) + 1)/2) + f(n), with f(n) a 16-periodic function with values {1, 18, 17, 18, 14, 18, 17, 19, 5, 18, 17, 18, 14, 19, 19, 19, ...}, as proved by Lawrence Sze.

A093681 Sequence contains no 3-term arithmetic progression, starting with 1, 28.

Original entry on oeis.org

1, 28, 29, 31, 32, 37, 38, 40, 41, 56, 58, 59, 64, 65, 67, 68, 82, 109, 110, 112, 113, 118, 119, 121, 122, 137, 139, 140, 145, 146, 148, 149, 244, 271, 272, 274, 275, 280, 281, 283, 284, 299, 301, 302, 307, 308, 310, 311, 325, 352, 353, 355, 356, 361, 362
Offset: 1

Views

Author

Ralf Stephan, Apr 09 2004

Keywords

Comments

a(1)=1, a(2)=28; a(n) is least k such that no three terms of a(1), a(2), ..., a(n-1), k form an arithmetic progression.

Links

Crossrefs

Cf. A004793, A033157, A093678, A093679, A093680, A092482.
Row 6 of array in A093682.

Formula

a(n) = (Sum_{k=1..n-1} (3^A007814(k) + 1)/2) + f(n), with f(n) a 16-periodic function with values {1, 27, 26, 27, 23, 27, 26, 27, 14, 28, 28, 28, 28, 28, 28, 28, ...}, n >= 1 (conjectured and checked up to n=1000).

A101886 Smallest natural number sequence without any length 4 equidistant arithmetic subsequences.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 9, 10, 11, 14, 15, 16, 18, 19, 20, 22, 24, 27, 28, 29, 31, 32, 35, 36, 37, 39, 41, 42, 43, 47, 48, 50, 51, 53, 55, 58, 60, 61, 63, 65, 66, 68, 70, 71, 72, 77, 78, 80, 82, 85, 86, 87, 89, 90, 91, 94, 95, 96, 98, 99, 100, 102, 103, 104, 107, 109, 110, 111, 114
Offset: 1

Views

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 20 2004

Keywords

Examples

			4 is out because of 1,2,3,4. 13 is out because of 1,5,9,13.

Crossrefs

Cf. A101887, A101884, A101888.
A selection of sequences related to "no three-term arithmetic progression": A003002, A003003, A003278, A004793, A005047, A005487, A033157, A065825, A092482, A093678, A093679, A093680, A093681, A093682, A094870, A101884, A101886, A101888, A140577, A185256, A208746, A229037.

A101888 Smallest natural number sequence without any length 5 equidistant arithmetic subsequences.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 22, 23, 24, 25, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 79, 80, 81, 82, 86, 87, 88, 90, 91, 92, 93, 95
Offset: 1

Views

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 20 2004

Keywords

Examples

			5 is out because of 1,2,3,4,5. 21 is out because of 1,6,11,16,21.

Crossrefs

Cf. A101889, A101884, A101886.
A selection of sequences related to "no three-term arithmetic progression": A003002, A003003, A003278, A004793, A005047, A005487, A033157, A065825, A092482, A093678, A093679, A093680, A093681, A093682, A094870, A101884, A101886, A101888, A140577, A185256, A208746, A229037.

A186776 Stanley Sequence S(0,2).

Original entry on oeis.org

0, 2, 3, 5, 9, 11, 12, 14, 27, 29, 30, 32, 36, 38, 39, 41, 81, 83, 84, 86, 90, 92, 93, 95, 108, 110, 111, 113, 117, 119, 120, 122, 243, 245, 246, 248, 252, 254, 255, 257, 270, 272, 273, 275, 279, 281, 282, 284, 324, 326, 327, 329, 333, 335, 336, 338, 351, 353, 354, 356, 360, 362, 363, 365, 729, 731, 732, 734, 738, 740
Offset: 1

Views

Author

N. J. A. Sloane, Mar 19 2011

Keywords

Comments

See A185256.
In ternary these numbers have 0's and 1's everywhere, except the last digit is either 0 or 2. [Tanya Khovanova, Nov 16 2013]
a(n) = A005836(n) + A000035(n). [Tanya Khovanova, Nov 16 2013]

Links

Crossrefs

Cf. A185256, A004793, A033160, A033163.

Programs

Formula

Equals A004793(n)-1, also A033160(n)-2, also A033163(n)-3. Note that A004793 has a recurrence.

A033160 Begins with (2, 4); avoids 3-term arithmetic progressions.

Original entry on oeis.org

2, 4, 5, 7, 11, 13, 14, 16, 29, 31, 32, 34, 38, 40, 41, 43, 83, 85, 86, 88, 92, 94, 95, 97, 110, 112, 113, 115, 119, 121, 122, 124, 245, 247, 248, 250, 254, 256, 257, 259, 272, 274, 275, 277, 281, 283, 284, 286, 326, 328, 329, 331, 335, 337, 338, 340, 353, 355, 356, 358, 362
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

a(n) = A186776(n)+2 = A004793(n)+1 = A033163(n)-1. Cf. A185256.

Programs

A033163 Begins with (3, 5) and avoids 3-term arithmetic progressions.

Original entry on oeis.org

3, 5, 6, 8, 12, 14, 15, 17, 30, 32, 33, 35, 39, 41, 42, 44, 84, 86, 87, 89, 93, 95, 96, 98, 111, 113, 114, 116, 120, 122, 123, 125, 246, 248, 249, 251, 255, 257, 258, 260, 273, 275, 276, 278, 282, 284, 285, 287, 327, 329, 330, 332, 336, 338, 339, 341, 354, 356, 357, 359, 363
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • Iacobescu, F. 'Smarandache Partition Type and Other Sequences.' Bull. Pure Appl. Sci. 16E, 237-240, 1997.
  • H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.

Links

Crossrefs

a(n) = A186776(n)+3 = A004793(n)+2 = A033160(n)+1. Cf. A185256.

A236697 First differences of A131741.

Original entry on oeis.org

1, 2, 6, 2, 16, 2, 6, 4, 26, 6, 10, 6, 12, 6, 20, 12, 18, 22, 14, 34, 6, 30, 8, 10, 26, 24, 6, 42, 10, 8, 4, 8, 22, 2, 34, 24, 8, 10, 54, 8, 42, 28, 6, 96, 26, 40, 14, 60, 4, 20, 30, 46, 26, 12, 42, 28, 2, 70, 8, 126, 4, 26, 34, 6, 42, 18, 96, 26, 48, 4
Offset: 1

Views

Author

Zak Seidov, Jan 30 2014

Keywords

Comments

Among first 10000 terms, the largest is a(7790) = 17412.

Links

Crossrefs

Cf. A003002, A003003, A003278, A004793, A005047, A005487, A033157, A065825, A092482, A093678, A093679, A093680, A093681, A093682, A094870, A101884, A101886, A101888, A131741, A140577, A185256, A208746, A229037.

Formula

a(n) = A131741(n+1) - A131741(n).

A267650 Stanley sequence S_4(0,3): lexicographic first increasing sequence with a(0) = 0, a(1) = 3 and no 4 terms in arithmetic progression.

Original entry on oeis.org

0, 3, 4, 5, 7, 8, 10, 11, 16, 17, 18, 20, 21, 27, 28, 29, 31, 32, 34, 35, 36, 53, 55, 56, 57, 60, 61, 62, 64, 67, 69, 75, 87, 91, 100, 101, 103, 104, 105, 108, 109, 110, 114, 116, 120, 125, 127, 128, 129, 132, 134, 135, 164, 168, 173, 174, 175, 177, 181, 182, 184, 188, 190
Offset: 0

Views

Author

M. F. Hasler, Jan 18 2016

Keywords

Comments

See A185256 for S(0,3) = S_3(0,3) and A266728 for S_5(0,3).

Links

Crossrefs

For other examples of Stanley Sequences see A005487, A005836, A187843, A188052, A188053, A188054, A188055, A188056, A188057, A266727, A266728.
See also A004793, A033160, A033163.

Programs

  • PARI
    a(n,show=1,L=4,v=[0,3], D=v->v[2..-1]-v[1..-2])={while(#v<=n, show&&print1(v[#v]", "); v=concat(v, v[#v]); while(v[#v]++, forvec(i=vector(L, j, [if(j1||next(2), 2); break)); if(type(show)=="t_VEC", v, v[n+1])} \\ 2nd (optional) arg: zero = silent, nonzero = verbose, vector (e.g. [] or [1]) = get the whole list [a(1..n)] as return value, else just a(n). - M. F. Hasler, Jan 18 2016
Previous Showing 11-19 of 19 results.

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

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