A160830 Integer part of the product of two consecutive primes divided by their sum.

1, 1, 2, 4, 5, 7, 8, 10, 12, 14, 16, 19, 20, 22, 24, 27, 29, 31, 34, 35, 37, 40, 42, 46, 49, 50, 52, 53, 55, 59, 64, 66, 68, 71, 74, 76, 79, 82, 84, 87, 89, 92, 95, 97, 98, 102, 108, 112, 113, 115, 117, 119, 122, 126, 129, 132, 134, 136, 139, 140, 143, 149, 154, 155, 157

Offset: 1

Author

Cino Hilliard, May 27 2009

Keywords

• nonn

Comments

The differences a(n+1) - a(n) appear to grow without bound while the difference 2 appears to occur infinitely often.

Examples

			a(5) = floor(prime(5)*prime(6)/(prime(5)+prime(6))) = 5.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001043, A006094.

Programs

Magma

[Floor(NthPrime(n)*NthPrime(n+1)/(NthPrime(n)+NthPrime(n+1))): n in [1..100]]; // G. C. Greubel, Apr 30 2018

Maple

a:= n-> (l-> floor(mul(i,i=l)/add(i,i=l)))([ithprime(n+i)$i=0..1]):
seq(a(n), n=1..65);  # Alois P. Heinz, Sep 20 2024

Mathematica

Table[Floor[Prime[n]*Prime[n+1]/(Prime[n] +Prime[n+1])], {n, 1, 100}] (* G. C. Greubel, Apr 30 2018 *)
Floor[Times@@#/Total[#]&/@Partition[Prime[Range[100]],2,1]] (* Harvey P. Dale, Sep 20 2024 *)

PARI

g(x) = p1=prime(x);p2=prime(x+1);y=p1*p2/(p1+p2);floor(y);
g1(n) = for(j=1,n,print1(g(j)","))

Formula

a(n) = floor(prime(n)*prime(n+1)/(prime(n)+prime(n+1))) where prime(.) = A000040(.).

a(n) = floor( A006094(n)/A001043(n) ). - R. J. Mathar, May 29 2009.

Extensions

Inserted "two" in definition - R. J. Mathar, May 29 2009