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.

A164566 Primes p such that 7*p-6 and 7*p+6 are also prime numbers.

Original entry on oeis.org

5, 11, 19, 31, 41, 61, 71, 109, 151, 211, 229, 269, 379, 419, 431, 439, 479, 619, 641, 709, 739, 809, 839, 971, 1009, 1069, 1229, 1259, 1319, 1361, 1439, 1451, 1499, 1531, 1579, 1669, 1801, 1879, 1889, 2011, 2111, 2239, 2269, 2381, 2411, 2551, 2579, 2591
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Keywords

Comments

Primes of the form A087681(k)/7, any index k.

Examples

			For p=5, both 7*5-6=29 and 7*5+6=41 are prime,
for p=11, both 7*11-6=71 and 7*11+6=83 are prime.

Links

Crossrefs

Cf. A106015, A125272, A127430, A046133, A087681, A136052, A023225.

Programs

  • Magma
    [p: p in PrimesUpTo(3000) | IsPrime(7*p-6) and IsPrime(7*p+6)]; // Vincenzo Librandi, Apr 09 2013
  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[7*p-6]&&PrimeQ[7*p+6],AppendTo[lst,p]], {n,6!}];lst
Select[Prime[Range[700]], And @@ PrimeQ/@{7 # + 6, 7 # - 6}&] (* Vincenzo Librandi, Apr 09 2013 *)
  • PARI
    is(n)=isprime(n) && isprime(7*n-6) && isprime(7*n+6) \\ Charles R Greathouse IV, Mar 28 2017

Formula

A136052 INTERSECT A023225. [R. J. Mathar, Aug 20 2009]

Extensions

Examples rephrased by R. J. Mathar, Aug 20 2009

A164568 Primes p such that 9*p-10 and 9*p+10 are prime numbers.

Original entry on oeis.org

3, 7, 11, 13, 29, 41, 53, 59, 67, 97, 109, 179, 223, 239, 263, 353, 389, 409, 461, 463, 557, 601, 613, 631, 673, 757, 773, 839, 857, 937, 967, 977, 1019, 1163, 1277, 1301, 1327, 1471, 1627, 1753, 1789, 1877, 1879, 2027, 2087, 2237, 2251, 2269, 2311, 2351
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Keywords

Examples

			9*3-10=17, 9*3+10=37, ...

Links

Crossrefs

Cf. A106015, A124098, A125272, A127430, A153768, A164566, A164567

Programs

  • Magma
    [p: p in PrimesUpTo(2500) |IsPrime(9*p-10) and IsPrime(9*p+10)]; // Vincenzo Librandi, Jun 30 2016
  • Maple
    filter:= n -> isprime(n) and isprime(9*n-10) and isprime(9*n+10):
select(filter, [seq(i,i=3..1000,2)]); # Robert Israel, Jun 29 2016
  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[9*p-10]&&PrimeQ[9*p+10],AppendTo[lst,p]],{n,2*6!}];lst
Select[Prime[Range[400]], PrimeQ[9 # - 10] && PrimeQ[9 # + 10] &] (* Vincenzo Librandi, Jun 30 2016 *)
Select[Prime[Range[400]],AllTrue[9#+{10,-10},PrimeQ]&] (* Harvey P. Dale, Dec 23 2023 *)
  • PARI
    forprime(p=3,1e4,if(isprime(9*p-10)&&isprime(9*p+10),print1(p",")))

Extensions

Edited by Charles R Greathouse IV, Nov 02 2009

A164567 Primes p such that 5*p-6 and 5*p+6 are prime numbers.

Original entry on oeis.org

5, 7, 13, 19, 29, 37, 41, 47, 79, 83, 97, 103, 149, 163, 211, 257, 293, 313, 359, 379, 401, 421, 449, 509, 523, 541, 547, 601, 643, 653, 673, 691, 701, 733, 821, 853, 883, 911, 929, 937, 1009, 1129, 1171, 1217, 1367, 1381, 1423, 1511, 1567, 1619, 1637, 1787
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Keywords

Comments

Primes of the form A087681(k)/5, any k [R. J. Mathar, Sep 17 2009]

Crossrefs

Cf. A106015, A124098, A125272, A127430, A164566

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[5*p-6]&&PrimeQ[5*p+6],AppendTo[lst,p]], {n,6!}];lst
Select[Prime[Range[300]],AllTrue[5#+{6,-6},PrimeQ]&] (* Harvey P. Dale, Jun 09 2022 *)

A164570 Primes p such that 8*p-3 and 8*p+3 are also prime numbers.

Original entry on oeis.org

2, 5, 7, 13, 47, 103, 107, 127, 163, 233, 293, 337, 383, 433, 443, 467, 503, 673, 677, 733, 797, 877, 1087, 1093, 1153, 1217, 1223, 1307, 1637, 1933, 2053, 2087, 2137, 2423, 2477, 2543, 2633, 2687, 2857, 2917, 3163, 3373, 3407, 3467, 3767, 3793, 3877
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Keywords

Comments

Subsequence of A023229. [R. J. Mathar, Aug 26 2009]
Primes of the form A087695(k)/8. [R. J. Mathar, Aug 26 2009]

Examples

			For p=2, 8*2-3=13 and 8*2+3=19 are prime numbers, which adds p=2 to the sequence
For p=5, 8*5-3=37 and 8*5+3=43 are prime numbers, which adds p=5 to the sequence.

Links

Crossrefs

Cf. A023212, A023217, A023224, A023230, A023239, A060212, A106015, A124098, A125272, A127430, A153768, A164566, A164567, A164568, A164569.

Programs

  • Magma
    [p: p in PrimesUpTo(3000) | IsPrime(8*p-3) and IsPrime(8*p+3)]; // Vincenzo Librandi, Apr 09 2013
  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[8*p-3]&&PrimeQ[8*p+3],AppendTo[lst,p]], {n,7!}];lst
Select[Prime[Range[1000]], And@@PrimeQ/@{8 # + 3, 8 # - 3}&] (* Vincenzo Librandi, Apr 09 2013 *)
Select[Prime[Range[1000]],AllTrue[8#+{3,-3},PrimeQ]&] (* Harvey P. Dale, May 05 2023 *)

Extensions

Comments turned into examples by R. J. Mathar, Aug 26 2009

A284531 Primes p such that 6p - 5 and 6p + 5 are consecutive primes.

Original entry on oeis.org

31, 41, 71, 97, 139, 193, 337, 349, 421, 487, 587, 619, 643, 701, 811, 827, 1021, 1051, 1093, 1217, 1249, 1259, 1471, 1571, 1721, 1747, 1861, 1949, 2087, 2131, 2383, 2521, 2549, 2591, 2957, 3023, 3083, 3209, 3529, 3613, 3779, 3833, 3947, 4283, 4409, 4451, 4481, 4483, 4567, 4591, 4733
Offset: 1

Views

Author

Zak Seidov, Mar 28 2017

Keywords

Comments

a(n + 1) = a(n) + 2 for n = 47, 386, 868, 1000, 1247, 1521, 1834, 2271, 2435, 2437, 2468, 2483, 2811, 2819, 2960, 3202, 3531, 3581, 5021, 5178, 5245, 5669, 6009, 6087, 6198, 6686, 7017, 7029, 7454, 7576, 7699, 8557, 8940, 9018, 10130, 10240, 10449, 10578, 10952, 11070, 11103, 11199, ...
E.g., a(42)=4481 and a(43)=4483.

Examples

			31*6 - 5 = 181 = A000040(42) and 31*6 + 5 = 191 = A000040(43).

Links

Crossrefs

Subsequence of A127430. Cf. A000040.

Programs

  • Maple
    filter:= p -> isprime(p) and isprime(6*p-5) and isprime(6*p+5) and not isprime(6*p-1) and not isprime(6*p+1):
select(filter, [seq(i,i=3..10000, 2)]); # Robert Israel, Apr 07 2017
  • Mathematica
    Select[Range[31,5000,2], PrimeQ[#] && PrimeQ[a = 6 # - 5] && NextPrime[a] == a + 10 &]
cp6Q[n_]:=Module[{p1=6n-5},PrimeQ[p1]&&NextPrime[p1]==6n+5]; Select[ Prime[ Range[ 1000]],cp6Q] (* Harvey P. Dale, Jun 05 2017 *)
Showing 1-5 of 5 results.

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