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

1,3

Comments

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

Links

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

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.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000040, A001043, A006094.

Sequence in context: A174799 A248566 A091627 * A363761 A363763 A189303

Adjacent sequences: A160827 A160828 A160829 * A160831 A160832 A160833

Keyword

nonn

Author

Cino Hilliard, May 27 2009

Extensions

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

Status

approved