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Let p1, p2 be first pair of consecutive primes with difference 2n; let p3, p4 be 2nd such pair; sequence gives "wadi" value p3-p1.
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%I #18 Nov 27 2020 06:49:50

%S 2,6,8,270,42,12,180,102,546,750,822,510,660,300,534,5208,7140,3302,

%T 7800,1476,18840,20706,9570,44960,13986,5862,4672,71118,14538,59370,

%U 156348,17688,59184,155736,1782,328694,110370,119616,93402,76116

%N Let p1, p2 be first pair of consecutive primes with difference 2n; let p3, p4 be 2nd such pair; sequence gives "wadi" value p3-p1.

%D Enoch Haga, Exploring Prime Numbers on Your PC, 2nd edition, 1998, ISBN 1-885794-16-9, Table 5, pp. 40-41.

%H Robert G. Wilson v, <a href="/A046728/b046728.txt">Table of n, a(n) for n = 1..201</a>

%F a(n) = A046789(n) - A000230(n). - _Robert G. Wilson v_, Nov 26 2020

%e First consecutive prime pair having difference 60 is p1=43331, p2=43391; next is p3=102701, p4=102761; so a(30)=102701-43331=59370.

%t Flatten[Table[Differences[First /@ Take[Select[Partition[Prime[Range[60000]], 2, 1], Differences[#] == {2 n} &], 2]], {n, 40}]] (* _Jayanta Basu_, Jun 27 2013 *)

%o (PARI) a(n)=my(k,p=2,p1);forprime(q=3,,if(q-p==2*n,if(k++>1,return(p-p1),p1=p));p=q) \\ _Charles R Greathouse IV_, Jun 27 2013

%Y Cf. A038460, A038343. a(i)=b(i)-c(i) where b(i) is A046789 and c(i) is A000230.

%K nonn

%O 1,1

%A _Enoch Haga_

%E More terms from _Jud McCranie_

%E a(31) inserted by _Jayanta Basu_, Jun 27 2013