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 1-5 of 5 results.

A126243 a(n) = smallest prime number p which is the arithmetic mean of n-th prime < p and n-th prime > p.

Original entry on oeis.org

5, 11, 11, 41, 29, 37, 53, 67, 131, 71, 97, 139, 127, 727, 193, 157, 191, 211, 191, 359, 307, 521, 349, 577, 571, 353, 307, 487, 347, 541, 571, 487, 541, 409, 947, 593, 563, 569, 787, 547, 587, 983, 587, 569, 587, 1223, 563, 557, 1213, 569, 563, 1381, 1213
Offset: 1

Views

Author

Artur Jasinski, Dec 21 2006

Keywords

Examples

			5 is the smallest prime p = prime(n) such that p = (prime(n-1)+prime(n+1))/2 (5 = (3+7)/2).

Links

Crossrefs

Cf. A006562, A119381, A126238-A126243.

Programs

  • Mathematica
    f[n_] := Block[{k = n + 1, p},While[p = (Prime[k - n] + Prime[k + n])/2; p != Prime[k], k++ ];p];Table[f[n], {n, 58}] (* Ray Chandler, Dec 27 2006 *)

Extensions

Extended by Ray Chandler, Dec 27 2006
Figure and b-file updated by Hans Havermann, Feb 07 2007

A126239 Primes of the form p = prime(n+1) such that prime(n) = (prime(n+3)+prime(n-1))/2.

Original entry on oeis.org

1013, 2791, 4003, 4933, 5437, 5503, 5521, 5843, 6037, 6529, 7109, 7823, 8087, 8161, 8363, 10093, 17021, 18253, 18307, 19753, 21143, 22777, 25031, 25343, 25933, 26683, 27277, 27407, 27793, 28433, 28621, 33151, 33749, 35507, 35527, 36457, 36781
Offset: 1

Views

Author

Artur Jasinski, Dec 21 2006

Keywords

Crossrefs

Cf. A006562, A119381, A126238-A126243.

Programs

  • Mathematica
    Prime@Select[Range[3, 4000], 2Prime[ # - 1] == Prime[ # - 2] + Prime[ # + 2] &] (* Ray Chandler, Dec 27 2006 *)

Extensions

Edited and extended by Ray Chandler, Dec 27 2006

A098031 Primes p such that p = (prime(n)+ prime(n+4))/2.

Original entry on oeis.org

11, 13, 17, 103, 107, 151, 179, 251, 409, 421, 491, 619, 701, 709, 739, 941, 1009, 1051, 1069, 1459, 1487, 1499, 1571, 1759, 1789, 1873, 2281, 2441, 2659, 2671, 2741, 2749, 2789, 2819, 2861, 3011, 3019, 3331, 3389, 3463, 3931, 4001, 4111, 4177, 4229, 4231
Offset: 1

Views

Author

Cino Hilliard, Sep 10 2004

Keywords

Comments

The union of sequences A179208, A118467, and A126238. - Irina Gerasimova, Jul 07 2013

Examples

			prime(3)=5,prime(3+4)=17. (5+17)/2 = 11.

Links

Programs

  • Mathematica
    Select[Table[(Prime[n]+Prime[n+4])/2,{n,800}],PrimeQ] (* Harvey P. Dale, Sep 29 2017 *)
  • PARI
    f(n,m) = for(x=1,n,y=prime(x)+prime(x+m);if(y%2==0 & isprime(y\2), print1(y\2",")))

A126240 Primes p such that p = prime(n+3)=(prime(n+6)+prime(n))/2.

Original entry on oeis.org

11, 29, 31, 41, 71, 211, 251, 349, 439, 461, 751, 1031, 1051, 1289, 1291, 1609, 1667, 1723, 2113, 2417, 2423, 2503, 2579, 2711, 2903, 3079, 3919, 3967, 4153, 4271, 4591, 4759, 4951, 5051, 5399, 5693, 6173, 6361, 6451, 6691, 6733, 7229, 7541, 7559, 7793
Offset: 1

Views

Author

Artur Jasinski, Dec 21 2006

Keywords

Links

Crossrefs

Cf. A006562, A119381, A126238-A126243.

Programs

  • Mathematica
    Do[If[(Prime[n + 6] + Prime[n])/2 == Prime[n + 3], Print[Prime[n + 3]]], {n, 1, 3000}]
Transpose[Select[Partition[Prime[Range[4000]],7,1],(First[#]+Last[#])/2==#[[4]]&]][[4]] (* Harvey P. Dale, Feb 16 2014 *)

Extensions

Extended by Ray Chandler, Dec 27 2006

A126242 Prime numbers p such that p = prime(n+4)=(prime(n+8)+prime(n))/2.

Original entry on oeis.org

41, 61, 71, 89, 181, 373, 397, 433, 449, 863, 907, 911, 937, 941, 983, 1193, 1259, 1931, 2243, 2251, 2447, 3359, 3361, 3823, 3851, 4057, 4093, 5231, 5297, 5417, 5813, 6421, 6619, 7013, 7151, 7487, 7583, 7907, 8171, 8537, 8563, 8573, 8581, 9157, 9257, 9377
Offset: 1

Views

Author

Artur Jasinski, Dec 21 2006

Keywords

Links

Crossrefs

Cf. A006562, A119381, A126238-A126243.

Programs

  • Mathematica
    Do[If[(Prime[n + 8] + Prime[n])/2 == Prime[n + 4], Print[Prime[n + 4]]], {n, 1, 3000}]
Transpose[Select[Partition[Prime[Range[1200]],9,1],(First[#]+Last[#])/2 == #[[5]]&]][[5]] (* Harvey P. Dale, Jul 18 2013 *)

Extensions

Extended by Ray Chandler, Dec 27 2006
Showing 1-5 of 5 results.

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

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