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 1-3 of 3 results.

A163385 Primes p such that 3(p-3)-1 and 3(p-3)+1 are twin primes.

Original entry on oeis.org

5, 7, 13, 17, 23, 37, 53, 67, 79, 83, 97, 107, 157, 193, 223, 277, 347, 353, 367, 433, 443, 479, 487, 499, 569, 577, 599, 647, 653, 773, 797, 853, 907, 937, 1087, 1103, 1123, 1259, 1277, 1367, 1409, 1423, 1427, 1549, 1553, 1747, 1889, 2069, 2153, 2237, 2267
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 25 2009

Keywords

Comments

In other words, primes p such that 3*(p-3) is a term of A014574. - Omar E. Pol, Aug 05 2009

Examples

			3*(5-3) = 6, 3*(7-3) = 12, 3*(13-3) = 30, ...

Links

Crossrefs

Cf. A163386, A163387, A163388. - Omar E. Pol, Aug 05 2009

Programs

  • Maple
    select(p -> isprime(p) and isprime(3*p-10) and isprime(3*p-8), [seq(i,i=3..10000,2)]); # Robert Israel, Nov 13 2016
  • Mathematica
    f1[n_]:=If[PrimeQ[n-1]&&PrimeQ[n+1],True,False]; f2[n_]:=If[f1[n]&&PrimeQ[n/3+3],True,False]; lst={};Do[If[f2[n],AppendTo[lst,n/3+3]],{n,8!}];lst
Select[Prime[Range[400]],AllTrue[3(#-3)+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 16 2017 *)

Extensions

Definition clarified and edited by Omar E. Pol, Aug 05 2009

A163387 Primes p such that 5(p-5)-1 and 5(p-5)+1 are twin primes.

Original entry on oeis.org

11, 17, 41, 53, 59, 89, 137, 167, 251, 263, 269, 431, 467, 563, 599, 677, 683, 809, 857, 1061, 1109, 1181, 1223, 1259, 1277, 1319, 1361, 1523, 1607, 1889, 1931, 1949, 2111, 2237, 2393, 2399, 2741, 3251, 3371, 3617, 3821, 3833, 3881, 4133, 4217, 4373, 4679
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 25 2009

Keywords

Comments

In other words, primes p such that 5*(p-5) is member of A014574. [From Omar E. Pol, Aug 05 2009]

Examples

			5*(11-5)=30, 5*(17-5)=60,...

Links

Crossrefs

Cf. A163385, A163386
Cf. A014574, A163388 [From Omar E. Pol, Aug 05 2009]

Programs

  • Mathematica
    f1[n_]:=If[PrimeQ[n-1]&&PrimeQ[n+1],True,False]; f2[n_]:=If[f1[n]&&PrimeQ[n/5+5],True,False]; lst={};Do[If[f2[n],AppendTo[lst,n/5+5]],{n,8!}];lst
Select[Prime[Range[700]],AllTrue[5(#-5)+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 18 2015 *)

Extensions

Definition clarified by Omar E. Pol, Aug 05 2009

A163388 Primes p such that 6*(p-6) is an average of a twin prime pair.

Original entry on oeis.org

7, 11, 13, 23, 29, 31, 53, 83, 101, 109, 113, 149, 181, 211, 223, 293, 331, 353, 379, 431, 449, 461, 571, 599, 643, 659, 661, 673, 709, 743, 919, 1021, 1039, 1051, 1123, 1151, 1231, 1249, 1319, 1429, 1439, 1483, 1553, 1579, 1583, 1619, 1723, 1931, 2069, 2143
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 25 2009

Keywords

Comments

Primes of the form 6+A014574(k)/6, any k.

Examples

			For p=7, 6*(7-6)=6 = A014574(2), which puts 7 into the sequence.
For p=11, 6*(11-6)=30 = A014574(5), which puts p=11 into the sequence.

Links

Crossrefs

Cf. A014574, A163385, A163386, A163387.

Programs

  • Mathematica
    f1[n_]:=If[PrimeQ[n-1]&&PrimeQ[n+1],True,False]; f2[n_]:=If[f1[n]&&PrimeQ[n/ 6+6],True,False]; lst={};Do[If[f2[n],AppendTo[lst,n/6+6]],{n,8!}]; lst

Extensions

Definition rephrased, reference to A014574 added by R. J. Mathar, Aug 02 2009
Showing 1-3 of 3 results.

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

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