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 1-10 of 11 results. Next

A072569 Odd interprimes.

Original entry on oeis.org

9, 15, 21, 39, 45, 69, 81, 93, 99, 105, 111, 129, 165, 195, 205, 217, 225, 231, 279, 309, 315, 351, 363, 381, 393, 399, 405, 441, 453, 459, 465, 473, 483, 489, 495, 501, 515, 615, 625, 645, 667, 675, 687, 705, 723, 741, 747, 759, 765, 771, 803, 825, 855, 861
Offset: 1

Views

Author

Marco Matosic, Jun 24 2002

Keywords

Comments

The interprimes (A024675) are those integers that lie at the midpoint between consecutive odd primes.

Links

Crossrefs

Odd members of A024675. Sequence is union of A072572 and A072573.
Cf. A024675, A072568.

Programs

  • Mathematica
    a = Table[ Prime[n], {n, 2, 200}]; b = {}; Do[d = (a[[n + 1]] - a[[n]])/2; If[ OddQ[ a[[n]] + d], b = Append[b, a[[n]] + d]], {n, 1, 198}]; b
Select[Plus @@@ Partition[Table[Prime[n], {n, 2, 100}], 2, 1]/2, OddQ]
Select[Mean/@Partition[Prime[Range[2,200]],2,1],OddQ] (* Harvey P. Dale, Jan 22 2019 *)

Extensions

Edited by N. J. A. Sloane and Robert G. Wilson v, Jun 27 2002

A072568 Even interprimes.

Original entry on oeis.org

4, 6, 12, 18, 26, 30, 34, 42, 50, 56, 60, 64, 72, 76, 86, 102, 108, 120, 134, 138, 144, 150, 154, 160, 170, 176, 180, 186, 192, 198, 228, 236, 240, 246, 254, 260, 266, 270, 274, 282, 288, 300, 312, 324, 334, 342, 348, 356, 370, 376, 386, 414, 420, 426, 432
Offset: 1

Views

Author

Marco Matosic, Jun 21 2002

Keywords

Comments

The interprimes (A024675) are those integers that lie at the midpoint between consecutive odd primes.

Links

Crossrefs

Even members of A024675.
Cf. A024675, A072569, A072570, A072571, A072572, A072573.

Programs

  • Mathematica
    Select[Plus @@@ Partition[Table[Prime[n], {n, 2, 100}], 2, 1]/2, EvenQ]

Extensions

Offset corrected by Amiram Eldar, Mar 23 2020

A072572 Odd interprimes divisible by 3.

Original entry on oeis.org

9, 15, 21, 39, 45, 69, 81, 93, 99, 105, 111, 129, 165, 195, 225, 231, 279, 309, 315, 351, 363, 381, 393, 399, 405, 441, 453, 459, 465, 483, 489, 495, 501, 615, 645, 675, 687, 705, 723, 741, 747, 759, 765, 771, 825, 855, 861, 879, 885, 897, 909, 915, 933
Offset: 1

Views

Author

Marco Matosic, Jun 25 2002

Keywords

Links

Crossrefs

Cf. A072569, A072573, A024675.

Programs

  • Mathematica
    a = Table[ Prime[n], {n, 2, 200}]; b = {}; Do[d = (a[[n + 1]] - a[[n]])/2; If[ OddQ[a[[n]] + d] && Mod[d, 3] != 0, b = Append[b, a[[n]] + d]], {n, 1, 198}]; b
Select[Mean/@Partition[Prime[Range[4,200]],2,1],OddQ[#]&&Divisible[ #,3]&] (* Harvey P. Dale, Oct 29 2013 *)

Extensions

Edited by N. J. A. Sloane and Robert G. Wilson v, Jun 27 2002
Corrected by T. D. Noe, Nov 01 2006

A124619 Odd interprimes divisible by 13.

Original entry on oeis.org

39, 195, 351, 741, 897, 1313, 1443, 1599, 2379, 2405, 2535, 2613, 2691, 2847, 3055, 3081, 3627, 3705, 4641, 4771, 5031, 5577, 5655, 5889, 5967, 6045, 6201, 6409, 6825, 6877, 6903, 7007, 7033, 7605, 7943, 8437, 8541, 8931, 8957, 9009, 9035, 9321, 9607
Offset: 1

Views

Author

Artur Jasinski, Dec 21 2006

Keywords

Links

Crossrefs

Cf. A072569, A072572, A072573, A126228, A126229, A126230, A124620, A126231, A124622, A126233.

Programs

  • Mathematica
    Do[If[OddQ[(Prime[n + 1] + Prime[n])/2] && Mod[(Prime[n + 1] + Prime[n])/2, 13] == 0, Print[(Prime[n + 1] + Prime[n])/2]], {n, 1, 3000}] (*Artur Jasinski*)
Select[(Total/@Partition[Prime[Range[1200]],2,1])/2,OddQ[#]&&Mod[#,13] == 0&] (* Harvey P. Dale, May 23 2019 *)

Extensions

Extended by Ray Chandler, Jan 09 2007

A124620 Odd interprimes divisible by 17.

Original entry on oeis.org

459, 765, 969, 1003, 1207, 1377, 1581, 1785, 2295, 2601, 2703, 3213, 3723, 3995, 4131, 4403, 4641, 4947, 5933, 5967, 6409, 6477, 6579, 6613, 6749, 6987, 7701, 8075, 8517, 9435, 9741, 9775, 9877, 9945, 10217, 10455, 10897, 10965, 11305, 11645
Offset: 1

Views

Author

Artur Jasinski, Dec 21 2006

Keywords

Links

Crossrefs

Cf. A072569, A072572, A072573, A126228, A126229, A126230, A124619, A126231, A124622, A126233.

Programs

  • Mathematica
    Do[If[OddQ[(Prime[n + 1] + Prime[n])/2] && Mod[(Prime[n + 1] + Prime[n])/2, 17] == 0, Print[(Prime[n + 1] + Prime[n])/2]], {n, 1, 3000}] (*Artur Jasinski*)
Select[Range[17,12000,34],!PrimeQ[#]&&#-NextPrime[#,-1]==NextPrime[#]-#&] (* Harvey P. Dale, Nov 18 2012 *)

Extensions

Extended by Ray Chandler, Jan 09 2007

A126228 Odd interprimes divisible by 5.

Original entry on oeis.org

15, 45, 105, 165, 195, 205, 225, 315, 405, 465, 495, 515, 615, 625, 645, 675, 705, 765, 825, 855, 885, 915, 1095, 1215, 1305, 1425, 1465, 1485, 1505, 1575, 1665, 1695, 1715, 1785, 1795, 1875, 1895, 1995, 2075, 2085, 2105, 2205, 2295, 2405, 2475, 2535, 2585
Offset: 1

Views

Author

Artur Jasinski, Dec 21 2006

Keywords

Links

Crossrefs

Cf. A072569, A072572, A072573, A126229, A126230, A124619, A124620, A126231, A124622, A126233.

Programs

  • Mathematica
    Do[If[OddQ[(Prime[n + 1] + Prime[n])/2] && Mod[(Prime[n + 1] + Prime[n])/2, 5] == 0, Print[(Prime[n + 1] + Prime[n])/2]], {n, 1, 3000}] (*Artur Jasinski*)
Select[Select[Mean/@Partition[Prime[Range[400]],2,1],OddQ],Divisible[#,5]&]  (* Harvey P. Dale, Feb 06 2011 *)

Extensions

Extended by Ray Chandler, Jan 09 2007

A126229 Odd interprimes divisible by 7.

Original entry on oeis.org

21, 105, 217, 231, 315, 399, 441, 483, 861, 987, 1113, 1197, 1281, 1449, 1491, 1505, 1575, 1715, 1785, 1827, 1869, 1995, 2121, 2191, 2205, 2247, 2303, 2541, 2667, 2709, 2751, 2835, 2933, 3045, 3073, 3129, 3213, 3255, 3353, 3381, 3423, 3465, 3675, 3885
Offset: 1

Views

Author

Artur Jasinski, Dec 21 2006

Keywords

Links

Crossrefs

Cf. A072569, A072572, A072573, A126228, A126230, A124619, A124620, A126231, A124622, A126233.

Programs

  • Mathematica
    Do[If[OddQ[(Prime[n + 1] + Prime[n])/2] && Mod[(Prime[n + 1] + Prime[n])/2, 7] == 0, Print[(Prime[n + 1] + Prime[n])/2]], {n, 1, 3000}]

Extensions

Extended by Ray Chandler, Jan 09 2007

A126230 Odd interprimes divisible by 11.

Original entry on oeis.org

99, 165, 231, 363, 473, 495, 759, 803, 825, 1089, 1243, 1485, 1551, 2277, 2453, 2475, 2541, 2585, 2783, 3399, 3465, 3531, 3795, 4521, 4587, 4697, 4785, 4807, 5093, 5203, 5577, 5841, 6831, 7007, 7315, 7381, 7425, 7689, 7755, 8437, 8635, 8679, 8855, 8877
Offset: 1

Views

Author

Artur Jasinski, Dec 21 2006

Keywords

Links

Crossrefs

Cf. A072569, A072572, A072573, A126228, A126229, A124619, A124620, A126231, A124622, A126233.

Programs

  • Mathematica
    Do[If[OddQ[(Prime[n + 1] + Prime[n])/2] && Mod[(Prime[n + 1] + Prime[n])/2, 11] == 0, Print[(Prime[n + 1] + Prime[n])/2]], {n, 1, 3000}]
Select[Mean/@Partition[Prime[Range[2,2000]],2,1],OddQ[#]&&Divisible[#,11]&] (* Harvey P. Dale, Mar 14 2021 *)

A126231 Odd interprimes divisible by 19.

Original entry on oeis.org

399, 741, 855, 969, 1197, 1425, 1995, 3021, 3705, 4085, 4731, 4807, 4883, 5415, 5529, 5833, 7315, 7695, 7847, 7923, 8075, 8341, 9063, 9177, 9215, 9823, 10317, 10431, 10507, 10545, 11077, 11115, 11267, 11305, 11457, 11685, 12483, 13167, 13623
Offset: 1

Views

Author

Artur Jasinski, Dec 21 2006

Keywords

Links

Crossrefs

Cf. A072569, A072572, A072573, A126228, A126229, A126230, A124619, A124620, A124622, A126233.

Programs

  • Maple
    select(t ->nextprime(t)+prevprime(t)=2*t, [seq(i,i=19..20000,38)]); # Robert Israel, Mar 17 2020
  • Mathematica
    Do[If[OddQ[(Prime[n + 1] + Prime[n])/2] && Mod[(Prime[n + 1] + Prime[n])/2, 19] == 0, Print[(Prime[n + 1] + Prime[n])/2]], {n, 1, 3000}]
Select[Mean/@Partition[Prime[Range[2000]],2,1],OddQ[#]&&Divisible[#,19]&] (* Harvey P. Dale, Jan 24 2014 *)

Extensions

Extended by Ray Chandler, Jan 09 2007

A126233 Smallest number k such that (prime(k+1)+prime(k))/2 is odd and divisible by n-th odd prime.

Original entry on oeis.org

4, 6, 8, 25, 12, 88, 78, 19, 121, 24, 29, 46, 31, 126, 186, 153, 156, 379, 197, 139, 280, 132, 285, 380, 155, 63, 334, 1005, 203, 75, 77, 516, 314, 445, 87, 1075, 93, 95, 1872, 254, 697, 1201, 270, 425, 429, 447, 304, 2187, 124, 488, 1153, 128, 335, 136, 547, 742
Offset: 1

Views

Author

Artur Jasinski, Dec 21 2006

Keywords

Links

Crossrefs

Cf. A072569, A072572, A072573, A126228, A126229, A126230, A124619, A124620, A126231, A124622.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, c},While[c = (Prime[k + 1] + Prime[k])/2; Mod[c, 2] == 0 || Mod[c, Prime[n + 1]] > 0, k++ ];k];Table[f[n], {n, 56}] (* Ray Chandler, Jan 09 2007 *)

Extensions

Edited and extended by Ray Chandler, Jan 09 2007
Showing 1-10 of 11 results. Next

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

Content is available under The OEIS End-User License Agreement.