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A304917 a(n) = prime(n)^n - primorial(n - 1). 1
1, 7, 119, 2371, 160841, 4824499, 410308643, 16983052531, 1801142961773, 420707010207331, 25408470426711601, 6582951805279545151, 925103094894275494511, 73885357039888240238239, 12063348337737606907045313, 3876269049503627062809380911 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is mostly composite but sometimes prime, whereas prime(n) - p#(n) is always composite. See A305076 for n such that a(n) is prime.

LINKS

Table of n, a(n) for n=1..16.

FORMULA

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

EXAMPLE

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

MAPLE

N:=15:

forX from 1 to N do

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

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

print(Y);

end do:

# Second Maple program

seq(ithprime(k)^k-mul(ithprime(i), i=1..k-1), k=1..15);  # Muniru A Asiru, Jul 08 2018

MATHEMATICA

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 *)

PROG

(PARI) a(n) = prime(n) ^ n - factorback(primes(n - 1)) \\ David A. Corneth, May 21 2018

CROSSREFS

Cf. A002110, A062457, A305076.

Sequence in context: A221031 A221323 A268300 * A113667 A192565 A171209

Adjacent sequences:  A304914 A304915 A304916 * A304918 A304919 A304920

KEYWORD

nonn

AUTHOR

David James Sycamore, May 20 2018

STATUS

approved

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Last modified January 21 16:54 EST 2020. Contains 331114 sequences. (Running on oeis4.)