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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. 0
0, 1, 2, 3, 4, 5, 9, 30, 96, 148, 171, 201, 246, 274, 294, 467, 543, 603, 614 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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.

LINKS

Table of n, a(n) for n=1..19.

FORMULA

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

EXAMPLE

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.

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

PROG

(PFGW & SCRIPT)

DIM nn, -1

DIM kk

DIMS tt

LABEL loopn

SET nn, nn+1

SET kk, -1

LABEL loopk

SET kk, kk+1

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

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

IF !(ISPRP || ISPRIME) THEN goto loopk

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

GOTO loopn

CROSSREFS

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

Sequence in context: A323289 A065885 A274331 * A092233 A115895 A116017

Adjacent sequences:  A177061 A177062 A177063 * A177065 A177066 A177067

KEYWORD

nonn

AUTHOR

Pierre CAMI, Dec 09 2010

STATUS

approved

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Last modified November 12 19:41 EST 2019. Contains 329078 sequences. (Running on oeis4.)