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.

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A075288 Interprimes (A024675) which are of the form s*prime, s=13.

Original entry on oeis.org

26, 39, 1313, 4771, 7033, 9607, 11947, 12233, 14963, 15613, 18707, 20527, 24323, 26507, 27443, 30823, 31057, 33917, 36257, 43277, 45383, 48061, 48347, 48997, 52039, 57083, 61477, 66547, 75283, 75491, 77207, 83863, 84383, 85787, 86567
Offset: 1

Views

Author

Zak Seidov, Sep 12 2002

Keywords

Comments

Interprimes of the form s*prime are in A075277-A075296 ( s = 2 - 21 ). Case s=1 is impossible.

Examples

			1313 is an interprime and 1313/13 = 101 is prime.

Links

Crossrefs

Cf. A024675, A075277-A075296.

Programs

  • Mathematica
    s=13; Select[Table[(Prime[n+1]+Prime[n])/2, {n, 2, 4000}], PrimeQ[ #/s]&]
Select[Mean/@Partition[Prime[Range[2,8500]],2,1],PrimeQ[#/13]&] (* Harvey P. Dale, Apr 29 2012 *)
  • PARI
    first(n) = {my(res = List(), p); forprime(p=2, oo, if(precprime(13*p) + nextprime(13*p) == 26*p, listput(res, 13*p); if(#res>=n, return(res))))} \\ David A. Corneth, Jul 26 2017

A075289 Interprimes which are of the form s*prime, s=14.

Original entry on oeis.org

42, 154, 266, 574, 994, 1106, 2674, 3206, 3514, 4382, 5306, 5446, 6538, 6706, 8666, 8834, 9814, 9926, 10654, 11494, 13174, 13594, 14266, 14434, 14546, 15274, 15806, 17486, 17906, 18214, 18242, 21994, 22358, 22694, 24094, 25858, 27314, 28406
Offset: 1

Views

Author

Zak Seidov, Sep 12 2002

Keywords

Comments

Interprimes of the form s*prime are in A075277-A075296 ( s = 2 - 21 ). Case s=1 is impossible.

Examples

			266 is an interprime and 266/14 = 19 is prime.

Links

Crossrefs

Cf. A075277-A075296.

Programs

  • Mathematica
    s=14; Select[Table[(Prime[n+1]+Prime[n])/2, {n, 2, 4000}], PrimeQ[ #/s]&]
Select[Mean/@Partition[Prime[Range[2,3100]],2,1],PrimeQ[#/14]&] (* Harvey P. Dale, Feb 24 2015 *)

A075292 Interprimes which are of the form s*prime, s=17.

Original entry on oeis.org

34, 1003, 1207, 5933, 6613, 6749, 10217, 10897, 18547, 18649, 22117, 23137, 23239, 25177, 34493, 38267, 40477, 43469, 44047, 49351, 54553, 58973, 60503, 62441, 66623, 67813, 71893, 76619, 79543, 80257, 80903, 85153, 86683, 87601, 89437
Offset: 1

Views

Author

Zak Seidov, Sep 12 2002

Keywords

Comments

Interprimes of the form s*prime are in A075277-A075296 ( s = 2 - 21 ). Case s=1 is impossible.

Examples

			1207 is an interprime and 1207/17 = 71 is prime.

Links

Crossrefs

Cf. A075277-A075296.

Programs

  • Mathematica
    s=17; Select[Table[(Prime[n+1]+Prime[n])/2, {n, 2, 4000}], PrimeQ[ #/s]&]
Select[Mean[#]&/@Partition[Prime[Range[9000]],2,1],PrimeQ[#/17]&] (* Harvey P. Dale, Apr 06 2016 *)

A075295 Interprimes which are of the form s*prime, s=20.

Original entry on oeis.org

60, 260, 1220, 1660, 1780, 3620, 4460, 4660, 6260, 6340, 6980, 7580, 11140, 13180, 13460, 14020, 14540, 15380, 16220, 18220, 19060, 20180, 21940, 22180, 23260, 26420, 28780, 29620, 30980, 31660, 33860, 35540, 37220, 38620, 39860, 40580
Offset: 1

Views

Author

Zak Seidov, Sep 12 2002

Keywords

Comments

Interprimes of the form s*prime are in A075277-A075296 ( s = 2 - 21 ). Case s=1 is impossible.

Examples

			260 is an interprime and 260/20 = 13 is prime.

Links

Crossrefs

Cf. A075277-A075296.

Programs

  • Maple
    P:= select(isprime,[seq(i,i=3..10000,2)]):
IP:= (P[1..-2]+P[2..-1])/~2:
select(t -> t mod 20 = 0 and isprime(t/20), IP); # Robert Israel, Dec 15 2024
  • Mathematica
    s=20; Select[Table[(Prime[n+1]+Prime[n])/2, {n, 2, 14000}], PrimeQ[ #/s]&]
Select[Total[#]/2&/@Partition[Prime[Range[5000]],2,1],PrimeQ[#/20]&] (* Harvey P. Dale, Dec 15 2023 *)

A074870 Smallest interprimes of the form n*prime.

Original entry on oeis.org

4, 6, 12, 15, 12, 21, 56, 18, 30, 473, 60, 26, 42, 30, 176, 34, 198, 4883, 60, 42, 154, 69, 72, 50, 754, 81, 56, 667, 60, 93, 64, 99, 102, 105, 72, 111, 76, 195, 120, 205, 462, 86, 1364, 225, 138, 3337, 144, 2303, 150, 102, 260, 1537, 108, 165, 1624, 399, 754
Offset: 2

Views

Author

Zak Seidov, Sep 12 2002

Keywords

Comments

Interprimes of the form n*prime are in A075277-A075296 ( n = 2 - 21 ). Case n=1 is impossible. First 20 terms in the sequence are first terms in A075277-A075296.

Examples

			a(8)=56 because 56 is the smallest interprime of the form 8*prime.

Crossrefs

Cf. A075277-A075296.

Extensions

a(50) corrected by Sean A. Irvine, Jan 31 2025

A075278 Interprimes which are of the form s*prime, s=3.

Original entry on oeis.org

6, 9, 15, 21, 39, 69, 93, 111, 129, 309, 381, 393, 453, 489, 501, 687, 723, 771, 879, 933, 939, 1011, 1167, 1299, 1527, 1563, 1569, 1839, 1941, 1983, 2157, 2217, 2229, 2271, 2391, 2463, 2661, 2811, 2859, 2913, 3039, 3099, 3189, 3453, 3459, 3651, 3849
Offset: 1

Views

Author

Zak Seidov, Sep 12 2002

Keywords

Comments

Interprimes which are of the form s*prime are in A075277-A075296 (s = 2-21). Case s = 1 is impossible.

Examples

			39 is an interprime and 39/3 = 13 is prime.

Crossrefs

Cf. A075277--A075296.

Programs

  • Mathematica
    s=3; Select[Table[(Prime[n+1]+Prime[n])/2, {n, 2, 1000}], PrimeQ[ #/s]&]

A075280 Interprimes which are of the form s*prime, s=5.

Original entry on oeis.org

15, 205, 515, 1465, 1795, 1895, 2105, 3265, 3505, 3665, 4105, 4415, 4535, 4555, 4685, 5045, 6185, 7115, 7835, 8135, 8185, 9655, 9865, 10085, 10645, 11015, 11405, 12085, 12295, 12385, 13235, 14395, 16045, 16355, 16735, 17065
Offset: 1

Views

Author

Zak Seidov, Sep 12 2002

Keywords

Comments

Interprimes which are of the form s*prime are in A075277-A075296 (s = 2-21). Case s = 1 is impossible.

Examples

			205 is an interprime and 205/5 = 41 is prime.

Crossrefs

Cf. A075277-A075296.

Programs

  • Mathematica
    s=5; Select[Table[(Prime[n+1]+Prime[n])/2, {n, 2, 1000}], PrimeQ[ #/s]&]

A075283 Interprimes which are of the form s*prime, s=8.

Original entry on oeis.org

56, 376, 1016, 1864, 2344, 2696, 3064, 3544, 3736, 4024, 4168, 5384, 5864, 6376, 7016, 8696, 8744, 9224, 9736, 9784, 13096, 14312, 15208, 15464, 15592, 16424, 16696, 17096, 19384, 19816, 20344, 21064, 21496, 22856, 23336, 23704, 26984
Offset: 1

Views

Author

Zak Seidov, Sep 12 2002

Keywords

Comments

Interprimes which are of the form s*prime are in A075277-A075296 (s = 2-21). Case s = 1 is impossible.

Examples

			1016 is an interprime and 1016/8 = 127 is prime.

Crossrefs

Cf. A075277-A075296.

Programs

  • Mathematica
    s=8; Select[Table[(Prime[n+1]+Prime[n])/2, {n, 2, 1000}], PrimeQ[ #/s]&]

A075286 Interprimes which are of the form s*prime, s=11.

Original entry on oeis.org

473, 803, 1243, 2453, 5093, 9097, 16753, 17897, 18953, 22297, 26147, 26807, 27247, 28369, 32197, 35387, 36773, 38797, 42163, 44803, 49423, 53933, 60533, 66077, 66319, 66803, 68189, 68233, 69157, 69773, 72083, 72347, 79343, 80663
Offset: 1

Views

Author

Zak Seidov, Sep 12 2002

Keywords

Comments

Interprimes of the form s*prime are in A075277-A075296 ( s = 2 - 21 ). Case s=1 is impossible.

Examples

			1243 is an interprime and 1243/11 = 113 is prime.

Crossrefs

Cf. A075277-A075296.

Programs

  • Mathematica
    s=11; Select[Table[(Prime[n+1]+Prime[n])/2, {n, 2, 4000}], PrimeQ[ #/s]&]

A075290 Interprimes which are of the form s*prime, s=15.

Original entry on oeis.org

30, 45, 105, 165, 195, 465, 615, 645, 705, 885, 915, 1095, 1695, 2085, 2685, 2955, 2985, 3165, 3345, 3495, 3615, 3945, 4065, 4155, 4755, 5055, 5235, 5505, 6645, 6735, 8445, 8655, 8805, 8985, 9465, 9885, 9915, 10155, 10245, 10635, 10785, 11085
Offset: 1

Views

Author

Zak Seidov, Sep 12 2002

Keywords

Comments

Interprimes of the form s*prime are in A075277-A075296 ( s = 2 - 21 ). Case s=1 is impossible.

Examples

			105 is an interprime and 105/15 = 7 is prime.

Crossrefs

Cf. A075277-A075296.

Programs

  • Mathematica
    s=15; Select[Table[(Prime[n+1]+Prime[n])/2, {n, 2, 4000}], PrimeQ[ #/s]&]
Previous Showing 11-20 of 23 results. Next

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