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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.

%I A177064 #16 May 15 2019 06:07:35
%S A177064 0,1,2,3,4,5,9,30,96,148,171,201,246,274,294,467,543,603,614
%N A177064 Primorial indices j such that P(j)#*2^k - 1 is a lower twin prime for the minimal k selected in A103782.
%C A177064 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.
%F A177064 {j: A002110(j)*2^A103782(j)-1 in A001359}.
%e A177064 P(0)# = 1, P(0)#*2^2 - 1 = 3, P(0)#*2^2 + 1 = 5 twin prime of 5 so a(1)=0;
%e A177064 P(1)# = 1*2, P(1)#*2^1 - 1 = 3, P(1)#*2^1 + 1 = 5 twin prime of 5 so a(2)=1;
%e A177064 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.
%p A177064 isA001359 := proc(n) isprime(n) and isprime(n+2) ; end proc:
%p A177064 A002110 := proc(n) mul(ithprime(i),i=1..n) ; end proc:
%p A177064 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:
%p A177064 isA177064 := proc(n) A002110(n)*2^A103782(n)-1 ; isA001359(%) ; end proc:
%p A177064 for n from 0 do if isA177064(n) then print(n) ; end if; end do: # _R. J. Mathar_, Dec 12 2010
%o A177064 (PFGW & SCRIPT)
%o A177064 DIM nn,-1
%o A177064 DIM kk
%o A177064 DIMS tt
%o A177064 LABEL loopn
%o A177064 SET nn,nn+1
%o A177064 SET kk,-1
%o A177064 LABEL loopk
%o A177064 SET kk,kk+1
%o A177064 SETS tt,%d,%d\,;p(nn);kk
%o A177064 PRP p(nn)#*2^kk-1,tt
%o A177064 IF !(ISPRP || ISPRIME) THEN goto loopk
%o A177064 PRP p(nn)#*2^kk+1,tt
%o A177064 GOTO loopn
%Y A177064 Cf. A001359, A103782, A103783, A176994, A177031.
%K A177064 nonn
%O A177064 1,3
%A A177064 _Pierre CAMI_, Dec 09 2010