

A031165


a(n) = prime(n+3)  prime(n).


16



5, 8, 8, 10, 8, 10, 12, 12, 14, 12, 12, 10, 12, 16, 14, 14, 12, 12, 12, 12, 16, 18, 18, 14, 10, 8, 10, 20, 22, 24, 12, 18, 14, 18, 14, 16, 16, 16, 14, 18, 14, 16, 8, 18, 26, 28, 18, 10, 12, 12, 18, 18, 22, 18, 14, 14, 12, 12, 16, 26, 28, 20, 10, 20, 24, 30, 18, 16, 12
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Comments from Jonathan Vos Post, Jan 22 2006 (Start): This sequence is the k=3 case of the family of sequences a(k,n) = prime(n+k)  prime(n). See A001223 and A031131 for k = 1 and 2.
The records in this sequence give A115401. The minimal value, after the anomalous initial values (5, 8, 8), is 8 which occurs iff n is an element of A007530 (prime quadruples: numbers n such that n, n+2, n+6, n+8 are all prime). (End)


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = prime(n+3)  prime(n). a(n) = A000040(n+3)  A000040(n).  Jonathan Vos Post, Jan 22 2006
a(n) = A034961(n+1)  A034961(n).  Zak Seidov, Nov 07 2012


EXAMPLE

a(1) = prime(4)  prime(1) = 7  2 = 5, which is the only odd element of this sequence.
a(2) = prime(5)  prime(2) = 11  3 = 8.
a(3) = prime(6)  prime(3) = 13  5 = 8.
a(4) = prime(7)  prime(4) = 17  7 = 10.
a(99) = prime(102)  prime(99) = 557  523 = 34.  Jonathan Vos Post, Jan 22 2006


MAPLE

a:= n> ithprime(n+3)ithprime(n): seq (a(n), n=1..80);


MATHEMATICA

t = Array[Prime, 75]; Drop[t, 3]  Drop[t, 3] (* Robert G. Wilson v *)


PROG

(MAGMA) [NthPrime(n+3)NthPrime(n): n in [1..100] ]; // Vincenzo Librandi, Apr 11 2011
(PARI) p=2; q=3; r=5; forprime(s=7, 1e3, print1(sp", "); p=q; q=r; r=s) \\ Charles R Greathouse IV, Nov 07 2012
(Haskell)
a031165 n = a031165_list !! (n1)
a031165_list = zipWith () (drop 3 a000040_list) a000040_list
 Reinhard Zumkeller, Aug 23 2015


CROSSREFS

Cf. A000040, A001223, A007530, A031131, A034961, A115401.
Cf. A031166, A031167, A031168, A031169, A031170, A031171, A031172.
Sequence in context: A200286 A073822 A198606 * A113729 A097523 A250123
Adjacent sequences: A031162 A031163 A031164 * A031166 A031167 A031168


KEYWORD

nonn


AUTHOR

Jeff Burch, Dec 11 1999


EXTENSIONS

Edited by R. J. Mathar and N. J. A. Sloane, Aug 11 2008


STATUS

approved



