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

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

Offset: 1

Author

Pierre CAMI, Dec 09 2010

Keywords

• nonn

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

Cf. A001359, A103782, A103783, A176994, A177031.

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}.