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.

A096177 Primes p such that primorial(p)/2 + 2 is prime.

Original entry on oeis.org

2, 3, 5, 7, 13, 29, 31, 37, 47, 59, 109, 223, 307, 389, 457, 1117, 1151, 2273, 9137, 10753, 15727, 25219, 26459, 29251, 30259, 52901, 194471
Offset: 1

Views

Author

Hugo Pfoertner, Jun 27 2004

Keywords

Comments

a(27) > 172000. - Robert Price, May 10 2019
Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 16 2019

Examples

			a(3)=7 because primorial(7)/2 + 2 = A070826(4) + 2 = 2*3*5*7/2 + 2 = 107 is prime.
		

Crossrefs

Cf. A070826, A096178 primes of the form primorial(p)/2+2, A096547 primes p such that primorial(p)/2-2 is prime, A067024 smallest p+2 that has n distinct prime factors, A014545 primorial primes, A087398.

Programs

  • Mathematica
    k = 1; Do[If[PrimeQ[n], k = k*n; If[PrimeQ[k/2 + 2], Print[n]]], {n, 2, 100000}] (* Ryan Propper, Jul 03 2005 *)
  • PARI
    P=1/2;forprime(p=2,1e4,if(isprime((P*=p)+2), print1(p", "))) \\ Charles R Greathouse IV, Mar 14 2011

Extensions

7 additional terms, corresponding to probable primes, from Ryan Propper, Jul 03 2005
Edited by T. D. Noe, Oct 30 2008
a(26) from Robert Price, May 10 2019
a(27) from Tyler Busby, Mar 17 2024

A096547 Primes p such that primorial(p)/2 - 2 is prime.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 23, 31, 41, 53, 71, 103, 167, 431, 563, 673, 727, 829, 1801, 2699, 4481, 6121, 7283, 9413, 10321, 12491, 17807, 30307, 31891, 71917, 172517
Offset: 1

Views

Author

Hugo Pfoertner, Jun 27 2004

Keywords

Comments

Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019
a(32) > 180000. - Tyler Busby, Mar 29 2024

Examples

			Prime 7 is a term because primorial(7)/2 - 2 = A034386(7)/2 - 2 = 2*3*5*7/2 - 2 = 103 is prime.
		

Crossrefs

Cf. A070826, A096177 primes p such that primorial(p)/2+2 is prime, A096178 primes of the form primorial(p)/2+2, A014545 primorial primes, A087398.
Cf. A034386.

Programs

  • Maple
    b:= proc(n) b(n):= `if`(n=0, 1, `if`(isprime(n), n, 1)*b(n-1)) end:
    q:= p-> isprime(p) and isprime(b(p)/2-2):
    select(q, [$1..500])[];
  • Mathematica
    k = 1; Do[k *= Prime[n]; If[PrimeQ[k - 2], Print[Prime[n]]], {n, 2, 3276}] (* Ryan Propper, Oct 25 2005 *)
    Prime[#]&/@Flatten[Position[FoldList[Times,Prime[Range[1000]]]/2-2,?PrimeQ]] (* _Harvey P. Dale, Jun 09 2023 *)

Extensions

5 more terms from Ryan Propper, Oct 25 2005
a(29)-a(31) from Tyler Busby, Mar 16 2024

A087398 Primes of the form primorial(P(k))/2-2.

Original entry on oeis.org

13, 103, 1153, 15013, 255253, 4849843, 111546433, 100280245063, 152125131763603, 16294579238595022363, 278970415063349480483707693, 11992411764462614086353260819346129198103, 481473710367991963528473107950567214598209565303106537707981745633
Offset: 1

Views

Author

Cino Hilliard, Oct 21 2003

Keywords

Comments

Twinmorial numbers are the partial products of twin primes. Sum of reciprocals = 0.08756985926348207565388288916..
The next term (a(14)) has 174 digits. - Harvey P. Dale, Mar 30 2013

Crossrefs

Cf. A096177 primes k such that primorial(k)/2+2 is prime, A096178 primes of the form primorial(k)/2+2, A096547 Primes k such that primorial(k)/2-2 is prime, A067024 smallest p+2 that has n distinct prime factors, A014545 primorial primes.

Programs

  • Mathematica
    Select[#/2-2&/@Rest[FoldList[Times,1,Prime[Range[100]]]],PrimeQ] (* Harvey P. Dale, Mar 30 2013 *)
  • PARI
    twimorial(n) = { s=0; p=3; forprime(x=5,n, if(isprime(x-2),c1++); p=p*x; if(isprime(p-2), print1(p-2","); c2++; s+=1.0/(p-2); ) ); print(); print(s) }
    
  • PARI
    v=[];pr=1; forprime(p=3,2357,pr*=p; if(ispseudoprime(pr-2),v=concat(v,pr-2))) \\ Charles R Greathouse IV, Feb 14 2011

Formula

Twins 3*5 = 15 = p+2. p=13.

Extensions

Description corrected by Hugo Pfoertner, Jun 25 2004
One more term (a(13)) added by Harvey P. Dale, Mar 30 2013
Showing 1-3 of 3 results.