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.

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

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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.
		

Crossrefs

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)

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

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Comments

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

Crossrefs

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

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Comments

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

Crossrefs

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

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Comments

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

Crossrefs

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

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Comments

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

Crossrefs

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 1-5 of 5 results.