login
a(n) = prime(n)^n - primorial(n - 1).
1

%I #31 Sep 18 2022 08:00:59

%S 1,7,119,2371,160841,4824499,410308643,16983052531,1801142961773,

%T 420707010207331,25408470426711601,6582951805279545151,

%U 925103094894275494511,73885357039888240238239,12063348337737606907045313,3876269049503627062809380911

%N a(n) = prime(n)^n - primorial(n - 1).

%F a(n) = A062457(n) - A002110(n-1).

%e a(1) = prime(1)^1 - primorial(0) = 2^1 - 1 = 1.

%p N:=15:

%p for X from 1 to N do

%p Z:=mul(ithprime(i),i=1..(X-1));

%p Y:=(ithprime(X)^X-Z);

%p print(Y);

%p end do:

%p # Second Maple program

%p seq(ithprime(k)^k-mul(ithprime(i),i=1..k-1),k=1..15); # _Muniru A Asiru_, Jul 08 2018

%t Fold[Append[#1, {#1 - #2, #2} & @@ {Prime[#2]^#2, Prime[#2 - 1] #1[[-1, -1]]}] &, {{1, 1}}, Range[2, 16]][[All, 1]] (* _Michael De Vlieger_, Jul 19 2018 *)

%o (PARI) a(n) = prime(n)^n - factorback(primes(n - 1)) \\ _David A. Corneth_, May 21 2018

%Y Cf. A002110, A062457, A305076 (n such that a(n) is prime).

%K nonn

%O 1,2

%A _David James Sycamore_, May 20 2018