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.

A174920 List of primes p1 such that (p1,p2) are twin primes where both 2*p1+p2 and p1+2*p2 are primes.

Original entry on oeis.org

3, 5, 59, 269, 1949, 2999, 6359, 11489, 11549, 14549, 18539, 19889, 21839, 31079, 32909, 32969, 33329, 33599, 42569, 42839, 50459, 53549, 58109, 68879, 70199, 74609, 79229, 80909, 93809, 96329, 98909, 104309, 109139, 114599, 121019, 125789
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Keywords

Comments

Terms >5 are congruent to 29 mod 30. - Zak Seidov, May 10 2012
Also 2*p1+p2 and p1+2*p2 are twin primes. - Zak Seidov, May 10 2012

Examples

			a(1)=3 because 3, 5 are twin primes and 2*3+5=11, 3+2*5=13 are also primes.

Links

Crossrefs

Cf. A001359, A174913, A174915, A174916, A174917, A177335.
Cf. A132929, A177336.

Programs

  • Magma
    [NthPrime(n): n in [1..12000] | forall{p: p in [NthPrime(n)+2,3*NthPrime(n)+2,3*NthPrime(n)+4] | IsPrime(p)}]; // Bruno Berselli, May 10 2012
  • Maple
    select(q -> isprime(q) and isprime(q+2) and isprime(3*q+2) and isprime(3*q+4), [3,5,seq(i,i=29..200000,30)]); # Robert Israel, May 06 2019
  • Mathematica
    lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[2*p1+p2]&&PrimeQ[p1+2*p2],AppendTo[lst,p1]],{n,8!}];lst

Formula

From Wesley Ivan Hurt, May 03 2022: (Start)
a(n) = A132929(n) - 1.
a(n) = A177336(n) - 2. (End)

A175914 Primes p such that p+2*q is prime, where q is the prime after p.

Original entry on oeis.org

3, 5, 7, 11, 13, 41, 43, 59, 89, 101, 103, 113, 127, 179, 181, 191, 193, 223, 241, 269, 277, 293, 307, 311, 313, 337, 359, 421, 431, 479, 491, 521, 599, 613, 631, 673, 773, 787, 821, 823, 863, 881, 883, 907, 911, 919, 929, 937, 953, 967, 1019, 1021, 1039, 1061, 1109, 1151, 1171
Offset: 1

Views

Author

Zak Seidov, Dec 05 2010

Keywords

Comments

A174915 gives lesser of twin primes in this sequence.
Values of p+2*q are in A094105. [Zak Seidov, Sep 07 2012]

Examples

			3 and 5 are consecutive primes, and 3+2*5 = 13 is prime. Hence 3 is in the sequence.
59 and 61 are consecutive primes, and 59+2*61 = 181 is prime. Hence 59 is in the sequence.

Links

Crossrefs

Cf. A094105, A114262, A174915, A001359.

Programs

  • Magma
    [p: p in PrimesUpTo(1200) | IsPrime(p+2*NextPrime(p))]; // Klaus Brockhaus, Dec 06 2010
  • Mathematica
    p = 3; Reap[Do[q = NextPrime[p]; If[PrimeQ[p + 2 q], Sow[p]]; p = q, {10^3}]][[2, 1]] (* Zak Seidov, Oct 14 2012 *)

A174916 Lesser of twin primes p1 such that p1 + p2^2 - p1^2 is a prime number.

Original entry on oeis.org

3, 5, 11, 17, 29, 71, 101, 281, 311, 419, 461, 521, 599, 617, 641, 659, 809, 827, 857, 881, 1019, 1061, 1277, 1289, 1319, 1607, 1721, 1949, 2027, 2111, 2141, 2309, 2339, 2381, 2591, 2729, 2801, 3329, 3557, 3581, 3767, 3851, 4049, 4127, 4157, 4217, 4229
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Keywords

Comments

3+(5^2-3^2)=3+16=19,..
Let x be the lesser of twin prime pairs. The sequence contains terms such that 5*x+4 is prime. - Harvey P. Dale, Sep 11 2012

Links

Crossrefs

Cf. A001359, A174913, A174915.

Programs

  • Mathematica
    lst={}; Do[p1=Prime[n]; p2=p1+2; If[PrimeQ[p2] && PrimeQ[p1+(p2^2-p1^2)], AppendTo[lst, p1]], {n, 1000}]; lst
With[{ltp=Transpose[Select[Partition[Prime[Range[600]],2,1],#[[2]]- #[[1]]==2&]][[1]]}, Select[ltp,PrimeQ[5#+4]&]] (* Harvey P. Dale, Sep 11 2012 *)

A174917 Lesser of twin primes p1 such that p2+(p2^2-p1^2) is a prime number.

Original entry on oeis.org

5, 11, 29, 41, 107, 137, 149, 197, 239, 347, 431, 461, 569, 599, 659, 809, 821, 1019, 1229, 1289, 1481, 1619, 1787, 1877, 1931, 2027, 2129, 2141, 2309, 2339, 2657, 2687, 2801, 2969, 3119, 3329, 3467, 3557, 3581, 4001, 4019, 4127, 4241, 4421, 4547, 4649
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Keywords

Comments

5+(7^2-5^2)=5+24=29,...

Links

Crossrefs

Cf. A001359, A174913, A174915, A174916

Programs

  • Mathematica
    lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[p2+(p2^2-p1^2)],AppendTo[lst,p1]],{n,4*6!}];lst
Select[Partition[Prime[Range[700]],2,1],#[[2]]-#[[1]]==2&& PrimeQ[ #[[2]]+ #[[2]]^2-#[[1]]^2]&][[All,1]] (* Harvey P. Dale, Dec 18 2021 *)

A174922 Lesser of twin primes p1 such that p1+(p2^2-p1^2) and p2+(p2^2-p1^2) are prime numbers.

Original entry on oeis.org

5, 11, 29, 461, 599, 659, 809, 1019, 1289, 2027, 2141, 2309, 2339, 2801, 3329, 3557, 3581, 4127, 4421, 4547, 5879, 6761, 10091, 10457, 10709, 13829, 15329, 18911, 20231, 21839, 23561, 23909, 26249, 26879, 27581, 27689, 27917, 28109, 30491
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Keywords

Comments

5+(7^2-5^2)=5+24=29; 7+(7^2-5^2)=7+24=31,..

Links

Crossrefs

Cf. A001359, A174913, A174915, A174916, A174917, A174920

Programs

  • Mathematica
    lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[p1+(p2^2-p1^2)]&&PrimeQ[p2+(p2^2-p1^2)],AppendTo[lst,p1]],{n,8!}];lst
prQ[{a_,b_}]:=Module[{c=b^2-a^2},AllTrue[{a+c,b+c},PrimeQ]]; Transpose[ Select[ Select[ Partition[Prime[Range[5000]],2,1],#[[2]]-#[[1]] == 2&], prQ]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 12 2015 *)

A174955 Lesser of twin primes p1 such that p1*p2+-6 are prime numbers.

Original entry on oeis.org

5, 11, 1061, 2111, 3371, 3851, 5867, 9461, 12251, 21491, 22037, 22481, 24917, 26681, 28277, 32141, 42641, 43607, 48731, 56477, 59417, 59627, 67271, 67757, 70487, 77417, 86531, 87221, 91127, 104147, 113621, 115151, 116687, 119291, 121577
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Keywords

Comments

5*7=35+-6 -> primes,..

Crossrefs

Cf. A001359, A174913, A174915, A174916, A174917, A174920, A174922

Programs

  • Mathematica
    lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[p1*p2+6]&&PrimeQ[p1*p2-6],(*Print[p1];*)AppendTo[lst,p1]],{n,8!}];lst

A174957 Lesser of twin primes p1 such that p1*p2-4 and p1*p2-6 are twin prime numbers.

Original entry on oeis.org

5, 11, 1031, 2711, 3851, 4421, 5867, 8837, 10067, 12041, 12251, 12611, 17957, 21491, 21521, 22037, 22481, 23537, 32141, 32411, 42641, 48311, 48731, 49367, 50261, 53231, 60167, 72167, 77417, 80147, 80447, 81047, 87641, 88337, 90527, 95231
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Keywords

Comments

5*7=35; 35-4=31; 35-6=29; 29,31 twin primes

Links

Crossrefs

Cf. A001359, A174913, A174915, A174916, A174917, A174920, A174922, A174955.

Programs

  • Mathematica
    lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[p1*p2-4]&&PrimeQ[p1*p2-6],(*Print[p1];*)AppendTo[lst,p1]],{n,8!}];lst
ltp[{a_,b_}]:=b-a==2&&AllTrue[a*b-{4,6},PrimeQ]; Select[Partition[Prime[ Range[ 10000]],2,1],ltp][[All,1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 07 2017 *)
Showing 1-7 of 7 results.

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