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.

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A177064 Primorial indices j such that P(j)#*2^k - 1 is a lower twin prime for the minimal k selected in A103782.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 9, 30, 96, 148, 171, 201, 246, 274, 294, 467, 543, 603, 614
Offset: 1

Views

Author

Pierre CAMI, Dec 09 2010

Keywords

Comments

For each j, the sequence A103782 constructs a prime of the form P(j)#*2^k - 1. If this is also a lower twin prime, then j is a term of this sequence.

Examples

			P(0)# = 1, P(0)#*2^2 - 1 = 3, P(0)#*2^2 + 1 = 5 twin prime of 5 so a(1)=0;
P(1)# = 1*2, P(1)#*2^1 - 1 = 3, P(1)#*2^1 + 1 = 5 twin prime of 5 so a(2)=1;
P(2)# = 1*2*3, P(2)#*2^1 - 1 = 11, P(2)#*2^1 + 1 = 13 twin prime of 11 so a(3)=2.
		

Crossrefs

Programs

  • Maple
    isA001359 := proc(n) isprime(n) and isprime(n+2) ; end proc:
    A002110 := proc(n) mul(ithprime(i),i=1..n) ; end proc:
    A103782 := proc(n) local m ; for m from 0 do if isprime(A002110(n)*2^m-1) then return m; end if; end do: end proc:
    isA177064 := proc(n) A002110(n)*2^A103782(n)-1 ; isA001359(%) ; end proc:
    for n from 0 do if isA177064(n) then print(n) ; end if; end do: # R. J. Mathar, Dec 12 2010

Formula

{j: A002110(j)*2^A103782(j)-1 in A001359}.

A103783 Primes of the form primorial P(k)*n-1 with minimal n, n>0, k>=2.

Original entry on oeis.org

5, 29, 419, 2309, 30029, 1021019, 19399379, 669278609, 38818159379, 601681470389, 14841476269619, 304250263527209, 235489703970060539, 1844669347765474229, 228124109340330313109, 24995884552004764307909
Offset: 1

Views

Author

Lei Zhou, Feb 15 2005

Keywords

Comments

Weak conjecture: sequence is defined for all k>=2; strong conjecture: n<(prime(k))^2;
Smallest prime p such that the prime factorization of p+1 contains the first n+1 primes. - R. J. Mathar, Jul 03 2012

Examples

			P(2)*1-1=5 is prime, so a(2)=5;
P(9)*3-1=669278609 is prime, so a(9)=669278609;
		

Crossrefs

Programs

  • Mathematica
    nmax = 2^2048; npd = 2; n = 2; npd = npd*Prime[n]; While[npd < nmax, tt = 1; cp = npd*tt - 1; While[(tt <= (Prime[n])^2) && (! (PrimeQ[cp])), tt = tt + 1; cp = npd*tt - 1]; Print[cp]; n = n + 1; npd = npd*Prime[n]]
Showing 1-2 of 2 results.