A060389 a(1)=p_1, a(2)=p_1 + p_1*p_2, a(3)=p_1 + p_1*p_2 + p_1*p_2*p_3, ... where p_i is the i-th prime.

2, 8, 38, 248, 2558, 32588, 543098, 10242788, 233335658, 6703028888, 207263519018, 7628001653828, 311878265181038, 13394639596851068, 628284422185342478, 33217442899375387208, 1955977793053588026278

Offset

1,1

Comments

Partial sums of the primorials A002110 starting from 2. - Charles R Greathouse IV, Feb 05 2014

All terms are even. From a(98) on, all terms are multiples of 523. - Charles R Greathouse IV, Feb 05 2014

The only values of n for which a(n)/2 is prime are: 3, 5, 7, 11, 15, 47, 49. The corresponding 7 primes are: 19, 1279, 271549, 103631759509, 314142211092671239, 826811434211869939736645732264127163964562391958563586838409421490271014424018927729, 41839936239750050346953677118447851613901200239299781782205558511980130628486398081201749. - Amiram Eldar, May 04 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Formula

a(n) = A002110(n-2)*A286624(n-1) + a(n-3), n >= 4. - Bob Selcoe, Oct 12 2017

a(n) = A276085(A070826(1+n)) = A084737(2+n)-2. - Antti Karttunen, Feb 06 2024

Example

a(4) = 248 because p_1 + p_1*p_2 + p_1*p_2*p_3 + p_1*p_2*p_3*p_4 = 2 + 6 + 30 + 210 = 248.
a(5) = 2558: A002110(3) = 30, A286624(4) = 85, a(2) = 8; 30*85 + 8 = 2558. - Bob Selcoe, Oct 12 2017

Maple

for n from 1 to 30 do printf(`%d, `, sum(product(ithprime(i), i=1..j), j=1..n)) od:

Mathematica

Accumulate[Denominator[Accumulate[1/Prime[Range[20]]]]] (* Alonso del Arte, Mar 21 2013 *)
Accumulate@ FoldList[Times, Prime@ Range@ 17] (* Michael De Vlieger, May 04 2017 *)

Prog

(PARI) a(n)=my(s, P=1); forprime(p=2, prime(n), s+=P*=p); s \\ Charles R Greathouse IV, Feb 05 2014

Crossrefs

Cf. A002110, A070826, A084737, A143293, A203008 [= A327860(a(n))], A276085, A286624.

Sequence in context: A293839 A355396 A265906 * A318917 A203122 A207157

Adjacent sequences: A060386 A060387 A060388 * A060390 A060391 A060392

Keyword

nonn

Author

Jason Earls, Apr 04 2001

Extensions

More terms from James A. Sellers, Apr 05 2001

Status

approved