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%I #20 Feb 12 2022 16:21:10
%S 0,3,6,13,39,167,900,4769,28389,180530,1209319,8398279,60070591,
%T 441296837,3314576488
%N Number of prime quadruples < 10^n, where a prime quadruple means 4 successive primes {p, p', p'', p'''} with p''' = p + 8.
%D J. Recreational Math., vol. 23, No. 2, 1991, p. 97.
%H <a href="/index/Pri#primepop">Index entries for sequences related to numbers of primes in various ranges</a>
%e For n=2 the quadruples are 3,5,7,11; 5,7,11,13; 11,13,17,19.
%p with(numtheory): x := 1229; t1 := [seq(ithprime(i),i=1..x)]; c := 0: for i from 1 to x-3 do if t1[i]+8 = t1[i+3] then c := c+1; fi; od: c; # the values of x to use are given by A006880.
%t x=168; a=Table[ Prime[ n ], {n, 1, x} ]; c=0; Do[ If[ a[ [ n ] ]+8==a[ [ n+2 ] ], c++ ], {n, 1, x-3} ]; # the values of x to use are given by A006880.
%Y Cf. A055737, A006880.
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Jun 09 2000
%E a(8)-a(9) from _Jud McCranie_, Oct 08 2000.
%E a(10)-a(12) from _Bert Dobbelaere_, Apr 17 2019
%E a(13)-a(15) from _Charles R Greathouse IV_, Feb 12 2022