A098206 A first order iteration: n-th term is obtained from (n-1)-th by adding n-th prime and then multiplying by the n-th prime; initial value is 1.

1, 12, 85, 644, 7205, 93834, 1595467, 30314234, 697227911, 20219610260, 626807919021, 23191893005146, 950867613212667, 40887307368146530, 1921703446302889119, 101850282654053126116, 6009166676589134444325

Offset: 1

Author

Labos Elemer, Oct 19 2004

Keywords

• nonn

Examples

			n=4: a(4)=(a(3)+7)*7=(85+7)*7=644.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..350

Crossrefs

Cf. A070826, A019461.

Programs

Maple

a:= n -> mul(ithprime(j),j=2..n) + add(ithprime(k)*mul(ithprime(j),j=k..n),k=2..n):
seq(a(n), n=1..30); # Robert Israel, Feb 12 2015

Mathematica

f[x_]:=(f[x-1]+Prime[x])*Prime[x];f[1]=0;Table[f[w], {w, 1, 25}]
nxt[{n_,a_}]:=Module[{p=Prime[n+1]},{n+1,p(a+p)}]; NestList[nxt,{1,1},20][[All,2]] (* Harvey P. Dale, Jun 18 2021 *)

Formula

a(n) = (a(n-1)+prime(n))*prime(n), a(1)=1.

a(n) = product(j=2..n, prime(j)) + sum(k=2..n, prime(k)*product(j=k..n, prime(j))). - Robert Israel, Feb 12 2015