A265184 a(n) = Sum_{k = 0..n} (-1)^k*prime(k)#, where prime(k)# is the prime factorial function.

1, -1, 5, -25, 185, -2125, 27905, -482605, 9217085, -213875785, 6255817445, -194304672685, 7226433462125, -297023830065085, 12785737501604945, -602104045086886465, 31987054432103158265, -1890773295722109480805, 115397608063684861502465

Offset

0,3

Comments

Alternating sum of primorial numbers.

abs(a(n)-1) is divisible by 6547 (the 845th prime) for all n >= 844. The only values of n for which abs(a(n)-1) is prime are: 2, 3, 5, 7, 19, 33, 125, 341, 571. The corresponding primes are 2, 13, 1063, 241303, 3871461971508291097188313, 3.576... * 10^52, 1.386... * 10^289, 5.823... * 10^968 and 1.227... * 10^1774. - Amiram Eldar, May 04 2017

Links

Table of n, a(n) for n=0..18.

OEIS Wiki, Primorial

Eric Weisstein's World of Mathematics, Primorial

Formula

a(n) = Sum_{k = 0..n} A033999(k)*A002110(k).

a(n) mod 5 = 0, for n > 1. - Altug Alkan, Dec 04 2015

Example

a(0) = 1;
a(1) = 1 - 2 = -1;
a(2) = 1 - 2 + 2*3 = 5;
a(3) = 1 - 2 + 2*3 - 2*3*5 = -25;
a(4) = 1 - 2 + 2*3 - 2*3*5 + 2*3*5*7 = 185;
a(5) = 1 - 2 + 2*3 - 2*3*5 + 2*3*5*7 - 2*3*5*7*11 = -2125, etc.

Mathematica

Table[Sum[(-1)^k Product[Prime@ j, {j, k}], {k, 0, n}], {n, 0, 18}]
(* Second program: *)
Accumulate@ FoldList[-#1 #2 &, 1, Prime@ Range@ 18] (* Michael De Vlieger, May 04 2017 *)

Crossrefs

Cf. A000040, A002110, A143293.

Sequence in context: A204461 A121144 A096684 * A096245 A294363 A294213

Adjacent sequences: A265181 A265182 A265183 * A265185 A265186 A265187

Keyword

sign

Author

Ilya Gutkovskiy, Dec 04 2015

Status

approved