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.

A087714 Primes p = prime(i) such that p(i)# - p(i+1) and p(i)# + p(i+1) are both primes, where p# = A002110.

Original entry on oeis.org

5, 13, 19, 367
Offset: 1

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Author

Pierre CAMI, Sep 28 2003

Keywords

Comments

Conjecture: there are only 4 primes in this sequence.

Examples

			2*3*5-7 = 23 is prime, 2*3*5+7 = 37 is prime.
		

Crossrefs

Programs

  • PARI
    isok(p) = {if (isprime(p), my(pp = prod(k=1, primepi(p), prime(k)), q = nextprime(p+1)); isprime(pp-q) && isprime(pp+q););} \\ Michel Marcus, Sep 20 2019
    
  • PARI
    my(pr=1); forprime(p=1, , pr=pr*p; if(ispseudoprime(pr-nextprime(p+1)) && ispseudoprime(pr+nextprime(p+1)), print1(p, ", "))) \\ Felix Fröhlich, Sep 20 2019

A087715 Table read by rows where i-th row consists of primes P of the form P=j*P(i)# -1 or P=j*P(i)# +1 with 0 < j < P(i+1). Here P(r)# = A002110.

Original entry on oeis.org

3, 3, 5, 5, 7, 11, 13, 17, 19, 23, 29, 31, 59, 61, 89, 149, 151, 179, 181, 211, 419, 421, 631, 839, 1049, 1051, 1259, 1471, 1889, 2099, 2309, 2311, 4621, 9239, 9241, 11549, 11551, 13859, 18481, 20789, 23099, 25409, 25411, 30029, 90089, 120121, 150151
Offset: 0

Views

Author

Pierre CAMI, Sep 29 2003

Keywords

Examples

			Table begins:
3,3,5,
5,7,11,13,17,19,23,
29,31,59,61,89,149,151,179,181,
211,419,421,631,839,1049,1051,1259,1471,1889,2099,
2309,2311,4621,9239,9241,11549,11551,13859,18481,20789,23099,25409,25411
		

Crossrefs

Programs

  • PARI
    {for(i=1,6, p=prod(j=1,i, prime(j)); for(j=1, prime(i+1)-1, c=j*p; if(isprime(c-1),print1(c-1 ",")); if(isprime(c+1),print1(c+1 ",")); ););}

Extensions

Edited by Ray Chandler, Sep 30 2003

A087716 Base-2 pseudoprimes (see A001567) of the form j*p(i)# - p(k) or j*p(i)# + p(k), p(i) and p(k) primes with p(i) < p(k) < p(i+1)^2 and 0 < j < p(i+1).

Original entry on oeis.org

341, 1387, 2047, 4681, 13747
Offset: 1

Views

Author

Pierre CAMI, Sep 29 2003

Keywords

Comments

Conjecture: sequence has only 5 terms. This has been checked for all i <= 150.

Examples

			   2*7#  -  79 =   341,
   7*7#  -  83 =  1387,
  10*7#  -  53 =  2047,
   2*11# +  61 =  4681,
   6*11# - 113 = 13747,
  13*7#  -  29 =  2701.
		

Crossrefs

# denotes primorials; see A002110.

Programs

  • PARI
    lst(lim)=my(p=2,P=1,v=List());forprime(q=3,lim,P*=p;forprime(r=q, q^2, for(j=1,q-1,if(j*P-r>340&&psp(j*P-r),listput(v,j*P-r)); if(psp(j*P+r),listput(v,j*P+r))));p=q);vecsort(Vec(v),,8) \\ Charles R Greathouse IV, Apr 12 2012

Extensions

Edited by David Wasserman, Apr 13 2006
Showing 1-3 of 3 results.