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a(0) = 1; a(n+1) = a(n) * (next prime larger than a(n)).
2

%I #18 Mar 19 2024 11:49:07

%S 1,2,6,42,1806,3270666,10697259354222,114431357691543566765996394,

%T 13094535623129987017538646614449662873664453962869814,

%U 171466863185420237392391564368967506501628543653753176958938044126997508808439363294403869833497610468982

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

%C 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

%e If n=1, then the prime immediately greater than n is 2. Hence the next number is n*p = 1*2 = 2.

%e If n=2, then the next prime is 3, so the next number in the sequence is 2*3=6.

%e If n=6, then the next prime is 7, so the next number in the sequence is 6*7=42.

%t 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 *)

%t NestList[# NextPrime[#]&,1,10] (* _Harvey P. Dale_, Oct 15 2016 *)

%o (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

%o (Python)

%o from itertools import islice

%o from sympy import nextprime

%o def A100016_gen(): # generator of terms

%o yield (a:=1)

%o while (a:=a*nextprime(a)): yield a

%o A100016_list = list(islice(A100016_gen(),10)) # _Chai Wah Wu_, Mar 19 2024

%Y Similar to A074839.

%Y Even more similar to A007018.

%K nonn

%O 0,2

%A _Parthasarathy Nambi_, Nov 18 2004

%E More terms from _Robert G. Wilson v_, Nov 23 2004