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 1-8 of 8 results.

A300898 Primes p such that p# + 4 is divisible by the next prime after p.

Original entry on oeis.org

2, 3, 11, 107
Offset: 1

Views

Author

Chai Wah Wu, Mar 14 2018

Keywords

Comments

p# is the primorial as defined in A002110. First 4 terms coincide with A079853.
a(5) > prime(1.4*10^6) = 22182343. - Robert Price, Apr 02 2018

Crossrefs

A300899 Primes p such that p#+2 is divisible by the next prime after p.

Original entry on oeis.org

547, 248119, 4085777
Offset: 1

Views

Author

Chai Wah Wu, Mar 14 2018

Keywords

Comments

p# is the primorial as defined in A002110.

Crossrefs

A341804 Primes p dividing (the product of the primes less than p)-1.

Original entry on oeis.org

2, 5, 11, 176078293
Offset: 1

Views

Author

Jeppe Stig Nielsen, Feb 20 2021

Keywords

Comments

The initial term 2 is included because the empty product minus 1 (which gives zero) is divisible by 2.

Examples

			The prime 11 is included because 2*3*5*7-1 is divisible by 11. Therefore, the last factor of the product, namely 7, is in A341812.
		

Crossrefs

Programs

  • PARI
    t=1;forprime(p=2,,((t-1)%p==0)&&print1(p,", ");t*=p)

A300900 Primes p such that p#-2 is divisible by the next prime after p.

Original entry on oeis.org

2, 5, 269, 277
Offset: 1

Views

Author

Chai Wah Wu, Mar 14 2018

Keywords

Comments

p# is the primorial as defined in A002110.
If it exists, a(5) > prime(10^7) = 179424673. - Robert Price, Mar 28 2018

Crossrefs

A341812 Primes p such that p#-1 is divisible by the next prime after p.

Original entry on oeis.org

3, 7, 176078267
Offset: 1

Views

Author

Jeppe Stig Nielsen, Feb 20 2021

Keywords

Comments

Here p# means A034386(p).
The next prime after p is then in A341804.

Examples

			The prime 7 is a member of this sequence because 2*3*5*7-1=209 is divisible by 11, the next prime immediately following 7.
11 is NOT a member of this sequence because 2*3*5*7*11-1=2309 is not divisible by 13 (leaves a remainder of 8), the next prime after 11.
		

Crossrefs

Programs

  • PARI
    isok(p) = if (isprime(p), my(a=Mod(1,nextprime(1+p))); forprime(q=2,p,a*=q); (a == 1)); \\ Michel Marcus, Mar 03 2021

A102747 Primes p(n) such that p(n)#+p(n+1) is divisible by p(n+2).

Original entry on oeis.org

2, 7, 103, 229561, 863833
Offset: 1

Views

Author

Max Alekseyev, Feb 09 2005

Keywords

Examples

			7 belongs to this sequence since 2*3*5*7+11 is divisible by 13.
		

Crossrefs

Programs

  • PARI
    { isgood(p) = local(r,p2,p3); p2=nextprime(p+1); p3=nextprime(p2+1); r=Mod(1,p3); forprime(q=1,p,r*=q); r+=p2; return(r==0); }

Extensions

863833 from Ryan Propper, Jan 07 2008

A302143 Primes p such that p# + 9 is divisible by the next prime after p.

Original entry on oeis.org

3, 13, 191, 857
Offset: 1

Views

Author

Robert Price, Apr 02 2018

Keywords

Comments

p# is the primorial as defined in A002110.
a(5) > Prime[1.4*10^6] = 22182343.

Crossrefs

A302144 Primes p such that p# - 9 is divisible by the next prime after p.

Original entry on oeis.org

5, 11, 113, 883, 7129561, 12553753
Offset: 1

Views

Author

Robert Price, Apr 02 2018

Keywords

Comments

p# is the primorial as defined in A002110.
a(7) > Prime[1.4*10^6] = 22182343.

Crossrefs

Showing 1-8 of 8 results.