A177064 - OEIS

%I #16 May 15 2019 06:07:35

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

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

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

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

%e 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 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 isA001359 := proc(n) isprime(n) and isprime(n+2) ; end proc:

%p A002110 := proc(n) mul(ithprime(i),i=1..n) ; end proc:

%p 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 isA177064 := proc(n) A002110(n)*2^A103782(n)-1 ; isA001359(%) ; end proc:

%p for n from 0 do if isA177064(n) then print(n) ; end if; end do: # _R. J. Mathar_, Dec 12 2010

%o (PFGW & SCRIPT)

%o DIM nn,-1

%o DIM kk

%o DIMS tt

%o LABEL loopn

%o SET nn,nn+1

%o SET kk,-1

%o LABEL loopk

%o SET kk,kk+1

%o SETS tt,%d,%d\,;p(nn);kk

%o PRP p(nn)#*2^kk-1,tt

%o IF !(ISPRP || ISPRIME) THEN goto loopk

%o PRP p(nn)#*2^kk+1,tt

%o GOTO loopn

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

%K nonn

%O 1,3

%A _Pierre CAMI_, Dec 09 2010