A177031
Exponents n for which P#*2^n-1 is a lower twin prime, where P is the prime associated with n in A176994.
Original entry on oeis.org
0, 1, 5, 7, 9, 12, 15, 17, 92, 130, 131, 154, 175, 189, 190, 236, 271, 290, 365, 372, 518, 558, 574, 635, 646, 748, 804, 829, 1066, 1197, 1236, 1559, 1941, 2112, 2324
Offset: 1
2*3*2^0-1=5, 2*3*2^0+1=7 twin prime of 5 so a(1)=0
2*3*2^1-1=11, 2*3*2^1+1=13 twin prime of 11 so a(2)=1
2*3*2^2-1=23 prime but not twin prime
2*3*2^3-1=47 prime but not twin prime
2*3*2^4-1=95 composite
2*3*5*2^4-1=479 prime but not twin prime
2*3*2^5-1=191, 2*3*2^5+1=193 twin prime of 191 so a(3)=5
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
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.
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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
Showing 1-2 of 2 results.
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