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 1-7 of 7 results.

A126238 Primes of the form p = prime(k) = (prime(k+3)+prime(k-1))/2.

Original entry on oeis.org

1009, 2789, 4001, 4931, 5431, 5501, 5519, 5839, 6029, 6521, 7103, 7817, 8081, 8147, 8353, 10091, 17011, 18251, 18301, 19751, 21139, 22769, 25013, 25339, 25931, 26681, 27271, 27397, 27791, 28429, 28619, 33149, 33739, 35491, 35521, 36451, 36779
Offset: 1

Views

Author

Artur Jasinski, Dec 21 2006

Keywords

Links

Crossrefs

Cf. A006562, A119381, A126239-A126243.

Programs

  • Mathematica
    Prime@Select[Range[2, 4000], 2Prime[ # ] == Prime[ # - 1] + Prime[ # + 3] &] (* Ray Chandler, Dec 27 2006 *)
Transpose[Select[Partition[Prime[Range[4000]],5,1],2#[[2]]==#[[5]]+#[[1]]&]][[2]] (* Harvey P. Dale, Jan 23 2013 *)

Extensions

Edited and extended by Ray Chandler, Dec 27 2006

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

A098029 Primes of the form (prime(k)+ prime(k+3))/2.

Original entry on oeis.org

7, 23, 37, 47, 67, 73, 233, 277, 353, 479, 613, 631, 647, 809, 1097, 1283, 1297, 1433, 1453, 1471, 1493, 1607, 1613, 1663, 1709, 1721, 1783, 1867, 1889, 1901, 1931, 1993, 2099, 2137, 2161, 2377, 2383, 2411, 2521, 2621, 2683, 2693, 2713, 2797, 2879, 3049
Offset: 1

Views

Author

Cino Hilliard, Sep 10 2004

Keywords

Comments

The union of {7}, A119381 and A117876. - Irina Gerasimova, Jul 11 2013

Examples

			prime(2)=3, prime(2+3)=11. (3+11)/2 = 7

Links

Programs

  • Mathematica
    Select[(#[[1]]+#[[4]])/2&/@Partition[Prime[Range[500]],4,1],PrimeQ] (* Harvey P. Dale, Nov 30 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",")))

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

A094933 Primes prime(k) such that (prime(k-1) + prime(k+1) + prime(k+2))/prime(k) = 3.

Original entry on oeis.org

127, 149, 431, 967, 1031, 1061, 1597, 2437, 2833, 2953, 3793, 5923, 6449, 6701, 6959, 7103, 8803, 11467, 11617, 11717, 11923, 12611, 13291, 13327, 13397, 13679, 13721, 14533, 14713, 15787, 16087, 17417, 17921, 18539, 20021, 21269, 21467, 22027
Offset: 1

Views

Author

Roger L. Bagula, Jun 17 2004

Keywords

Examples

			127 is OK since 127 is p(31) and (p(n-1) + p(n+1)+ p(n+2))/p(n)=(113+131+137)/127=3. - _Zak Seidov_, Aug 04 2006

Links

Crossrefs

Cf. A119381.

Programs

  • MATLAB
    p=primes(30000);
m=1;
for u=2:length(p)-2
  if p(u-1)+p(u+1)+p(u+2)-3*p(u)==0;
     sol(m)=p(u);  m=m+1;
  end
end
sol % Marius A. Burtea, May 06 2019
  • Magma
    [NthPrime(n):n in [2..3000]|NthPrime(n-1)+NthPrime(n+1)+NthPrime(n+2)- 3*NthPrime(n) eq 0]; // Marius A. Burtea, May 06 2019
  • Maple
    p:= 2: q:= 3: r:= 5: s:= 7:
count:= 0: Res:= NULL:
while count < 100 do
  if p + r + s = 3*q then count:= count+1; Res:= Res, q fi;
  p:= q; q:= r; r:= s; s:= nextprime(s)
od:
Res; # Robert Israel, May 06 2019
  • Mathematica
    a=Table[If[(Prime[n-3]+Prime[n-2]+Prime[n-1]+Prime[n])/4-Prime[n-2]==0, Prime[n-2], 0], {n, 4, 2004}] a0=Delete[Union[Sort[a]], 1]
Select[Prime[Range[2,3000]],Prime[PrimePi[ # ]-1]+Prime[PrimePi[ # ]+1]+Prime[PrimePi[ # ]+2]==3#&] (* Zak Seidov, Aug 04 2006 *)

Extensions

More terms from Zak Seidov, Aug 04 2006
Edited by N. J. A. Sloane, Aug 08 2008

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 1-7 of 7 results.

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

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