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A332731
a(n) is the smallest positive k such that n!*prime(n) - k is a prime.
1
1, 1, 1, 1, 11, 11, 1, 13, 1, 17, 1, 1, 53, 17, 1, 29, 23, 31, 23, 1, 29, 67, 31, 31, 43, 29, 181, 1, 83, 41, 101, 79, 179, 79, 43, 83, 47, 83, 163, 79, 53, 73, 59, 67, 347, 223, 67, 53, 97, 1, 157, 73, 1, 229, 101, 1, 263, 103, 101, 163, 139, 599, 103, 197, 73, 433, 313, 73
OFFSET
2,5
COMMENTS
Equivalently, a(n) = n!*prime(n) minus the previous prime.
FORMULA
a(n) = n!*prime(n) - A007917(n!*prime(n)).
EXAMPLE
For n=3, n!*prime(n) = 3!*prime(3) = 6*5 = 30, and the largest prime < 30 is 29, so a(3) = 30 - 29 = 1.
MATHEMATICA
Table[With[{c=n!Prime[n]}, c-NextPrime[c, -1]], {n, 2, 70}] (* Harvey P. Dale, Sep 01 2024 *)
PROG
(PARI) a(n) = my(x=n!*prime(n)); x - precprime(x); \\ Michel Marcus, Feb 22 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved