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

1,2

Links

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

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

Example

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

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 *)

Crossrefs

Cf. A070826, A019461.

Sequence in context: A095267 A118017 A225785 * A104911 A283119 A091119

Adjacent sequences: A098203 A098204 A098205 * A098207 A098208 A098209

Keyword

nonn

Author

Labos Elemer, Oct 19 2004

Status

approved