A185371 Product of two consecutive primes divided by the next prime and rounded down.

1, 2, 3, 5, 8, 11, 14, 15, 21, 24, 27, 35, 37, 38, 42, 51, 53, 57, 65, 65, 69, 73, 76, 85, 95, 97, 101, 103, 96, 109, 121, 129, 127, 137, 143, 145, 153, 157, 161, 171, 169, 179, 187, 191, 185, 188, 207, 221, 223, 223, 231, 229, 235, 245, 251, 261, 263, 267, 275

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000 [Offset adapted by Georg Fischer, Feb 10 2026]

Formula

a(n) = floor(prime(n)*prime(n+1)/prime(n+2)), where prime(n) is the n-th prime.

For n > 3, prime(n)/2 < a(n) < prime(n). prime(n) - a(n) << log(n)^2 under Cramer's conjecture. Weaker estimates follow from the Prime Number Theorem. - Charles R Greathouse IV, Jan 26 2012

Example

a(1) = floor(2*3/5) = 1.
a(2) = floor(3*5/7) = 2.
a(3) = floor(5*7/11) = 3.

Mathematica

Table[Floor[Prime[n]*Prime[n + 1]/Prime[n + 2]], {n, 1, 50}] (* G. C. Greubel, Jun 28 2017 *)
Floor[(#[[1]]#[[2]])/#[[3]]]&/@Partition[Prime[Range[70]], 3, 1] (* Harvey P. Dale, Jan 12 2026 *)

Prog

(PARI) my(p=2, q=3); forprime(r=5, 1e3, print1(p*q\r, ", "); p=q; q=r) \\ Charles R Greathouse IV, Jan 26 2012

Crossrefs

Sequence in context: A228855 A171048 A209292 * A071894 A301892 A271876

Adjacent sequences: A185368 A185369 A185370 * A185372 A185373 A185374

Keyword

nonn

Author

Tyler Carrico, Jan 26 2012

Extensions

a(14)-a(15) corrected, a(16)-a(59) from Charles R Greathouse IV, Jan 26 2012

Offset changed to 1 by Georg Fischer, Feb 10 2026

Status

approved