A055738 Number of prime quadruples < 10^n, where a prime quadruple means 4 successive primes {p, p', p'', p'''} with p''' = p + 8.
0, 3, 6, 13, 39, 167, 900, 4769, 28389, 180530, 1209319, 8398279, 60070591, 441296837, 3314576488
Offset: 1
Examples
For n=2 the quadruples are 3,5,7,11; 5,7,11,13; 11,13,17,19.
References
- J. Recreational Math., vol. 23, No. 2, 1991, p. 97.
Programs
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Maple
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.
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Mathematica
x=168; a=Table[ Prime[ n ], {n, 1, x} ]; c=0; Do[ If[ a[ [ n ] ]+8==a[ [ n+3 ] ], c++ ], {n, 1, x-3} ]; c (* The values of x to use are given by A006880. *)
Extensions
a(8)-a(9) from Jud McCranie, Oct 08 2000.
a(10)-a(12) from Bert Dobbelaere, Apr 17 2019
a(13)-a(15) from Charles R Greathouse IV, Feb 12 2022