A100016 a(0) = 1; a(n+1) = a(n) * (next prime larger than a(n)).

1, 2, 6, 42, 1806, 3270666, 10697259354222, 114431357691543566765996394, 13094535623129987017538646614449662873664453962869814, 171466863185420237392391564368967506501628543653753176958938044126997508808439363294403869833497610468982

Offset: 0

Author

Parthasarathy Nambi, Nov 18 2004

Keywords

• nonn

Comments

Terms are very close to A007018(n), with equality for the first 5 terms. Indeed, sequence A007018 is defined like the present sequence, with nextprime(a(n)) replaced by a(n)+1. - M. F. Hasler, May 20 2019

Examples

			If n=1, then the prime immediately greater than n is 2. Hence the next number is n*p = 1*2 = 2.
If n=2, then the next prime is 3, so the next number in the sequence is 2*3=6.
If n=6, then the next prime is 7, so the next number in the sequence is 6*7=42.
		

Crossrefs

Similar to A074839.

Even more similar to A007018.

Programs

Mathematica

a[0] = 1; a[n_] := a[n - 1]*NextPrime[a[n - 1]]; Table[ a[n], {n, 0, 9}] (* Robert G. Wilson v, Nov 23 2004 *)
NestList[# NextPrime[#]&,1,10] (* Harvey P. Dale, Oct 15 2016 *)

PARI

(nxt_A100016(n)=n*nextprime(n+1)); A100016_vec=vector(10,i,t=if(i>1,nxt_A100016(t),1)) \\ M. F. Hasler, May 20 2019

Python

from itertools import islice
from sympy import nextprime
def A100016_gen(): # generator of terms
    yield (a:=1)
    while (a:=a*nextprime(a)): yield a
A100016_list = list(islice(A100016_gen(),10)) # Chai Wah Wu, Mar 19 2024

Extensions

More terms from Robert G. Wilson v, Nov 23 2004