# [seqfan] A173088 edited

Klaus Brockhaus klaus-brockhaus at t-online.de
Mon Mar 1 17:20:17 CET 2010

```Seqfans,

I tried to understand and edit A173088, but I get a sequence that has
very little in common with the original sequence. So maybe I made a
mistake, maybe the author stumbled over his shorthand notation. In the
original definition
%N A173088 6*(A002822(n+5/2-+5/2)-+1 are all twin primes.
a closing parenthesis is obviously missing; the only place to insert it
that makes sense seems after the "n". - I made the example very expicit
and added a second one. For a final version they ought to be condensed
of course. - The MAGMA program I used for computing the sequence is also
given below.

Could some seqfan please check this?

Thanks and regards
Klaus

Edited version:

%I A173088
%S A173088
2,4,5,7,9,11,14,16,18,22,25,32,35,36,38,43,47,52,60,62,64,67,69,74,80,
%T A173088
86,87,88,93,99,104,107,110,111,117,140,146,152,155,167,170,183,188,190,
%U A173088
196,205,206,210,211,213,215,218,233,235,251,252,258,268,275,301,313
%N A173088 Numbers n such that (6*p-1, 6*p+1) and (6*(p+5)-1, 6*(p+5)+1)
are twin prime pairs, where p is A002822(n).
%e A173088 A002822(2) = 2. 2 is in the sequence because
6*(A002822(2)+0)-1 = 6*2-1 = 12-1 = 11 is prime, 6*(A002822(2)+0)+1 =
6*2-1 = 12+1 = 13 is prime, 6*(A002822(2)+5)-1 = 6*7-1 = 42-1 = 41 is
prime and 6*(A002822(2)+5)+1 = 6*7+1 = 42+1 = 43 is prime.
%e A173088 A002822(4) = 5. 4 is in the sequence because
6*(A002822(4)+0)-1 = 6*5-1 = 30-1 = 29 is prime, 6*(A002822(4)+0)+1 =
6*5+1 = 30+1 = 31 is prime, 6*(A002822(2)+5)-1 = 6*10-1 = 60-1 = 59 is
prime and 6*(A002822(2)+5)+1 = 6*10+1 = 60+1 = 61 is prime.
%Y A173088 Cf. A002822 (numbers n such that 6*n-1, 6*n+1 are twin primes).
%K A173088 nonn,new
%O A173088 1,1

--------------------------------------------------------------------------------------------------------
T:=[ k: k in [1..3000] | IsPrime(6*k-1) and IsPrime(6*k+1) ]; //A002822
[ n: n in [1..#T] | IsPrime(6*p-1) and IsPrime(6*p+1) and IsPrime(6*q-1)
and IsPrime(6*q+1) where q is p+5 where p is T[n] ];

```

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