A007811 Numbers k for which 10k+1, 10k+3, 10k+7 and 10k+9 are primes.

1, 10, 19, 82, 148, 187, 208, 325, 346, 565, 943, 1300, 1564, 1573, 1606, 1804, 1891, 1942, 2101, 2227, 2530, 3172, 3484, 4378, 5134, 5533, 6298, 6721, 6949, 7222, 7726, 7969, 8104, 8272, 8881, 9784, 9913

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = 3*A014561(n) + 1. - Zak Seidov, Sep 21 2009

Maple

for n from 1 to 10000 do m := 10*n: if isprime(m+1) and isprime(m+3) and isprime(m+7) and isprime(m+9) then print(n); fi: od: quit

Mathematica

Select[ Range[ 1, 10000, 3 ], PrimeQ[ 10*#+1 ] && PrimeQ[ 10*#+3 ] && PrimeQ[ 10*#+7 ] && PrimeQ[ 10*#+9 ]& ]
Select[Range[15000], And @@ PrimeQ /@ ({1, 3, 7, 9} + 10#) &] (* Ray Chandler, Jan 12 2007 *)

Prog

(Magma) [n: n in [0..10000] | forall{10*n+r: r in [1, 3, 7, 9] | IsPrime(10*n+r)}]; // Bruno Berselli, Sep 04 2012
(PARI) p=2; q=3; r=5; forprime(s=7, 1e5, if(s-p==8 && r-p==6 && q-p==2 && p%10==1, print1(p", ")); p=q; q=r; r=s) \\ Charles R Greathouse IV, Mar 21 2013
(Haskell)
a007811 n = a007811_list !! (n-1)
a007811_list = map (pred . head) $ filter (all (== 1) . map a010051') $
   iterate (zipWith (+) [10, 10, 10, 10]) [1, 3, 7, 9]
-- Reinhard Zumkeller, Jul 18 2014
(Perl) use ntheory ":all"; my @s = map { ($_-1)/10 } sieve_prime_cluster(10, 1e9, 2, 6, 8); say for @s; # Dana Jacobsen, May 04 2017

Crossrefs

Cf. A024912, A102338, A102342, A102700, A007530, A014561, A008471, A032352, A216292, A216293, A125855.

Cf. A010051, A245304, A245305.

Sequence in context: A023109 A255530 A146091 * A255764 A181957 A181898

Adjacent sequences: A007808 A007809 A007810 * A007812 A007813 A007814

Keyword

nonn

Author

N. J. A. Sloane and J. H. Conway, Mar 15 1996

Status

approved