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A304917
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a(n) = prime(n)^n - primorial(n - 1).
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1
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1, 7, 119, 2371, 160841, 4824499, 410308643, 16983052531, 1801142961773, 420707010207331, 25408470426711601, 6582951805279545151, 925103094894275494511, 73885357039888240238239, 12063348337737606907045313, 3876269049503627062809380911
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..16.
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FORMULA
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a(n) = A062457(n) - A002110(n-1).
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EXAMPLE
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a(1) = prime(1)^1 - primorial(0) = 2^1 - 1 = 1.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = prime(n) ^ n - factorback(primes(n - 1)) \\ David A. Corneth, May 21 2018
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CROSSREFS
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Cf. A002110, A062457, A305076.
Sequence in context: A221031 A221323 A268300 * A113667 A192565 A171209
Adjacent sequences: A304914 A304915 A304916 * A304918 A304919 A304920
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KEYWORD
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nonn
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AUTHOR
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David James Sycamore, May 20 2018
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STATUS
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approved
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