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A346425
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a(n) is the greatest number k such that k! <= prime(n).
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1
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2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
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OFFSET
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1,1
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COMMENTS
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Terms 2, 3, 4, 5, ... appear respectively 3, 6, 21, 98, ... times consecutively; indeed, 2 appears A061232(1) + A061232(2) times, then every m >= 3 appears A061232(m) times.
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LINKS
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FORMULA
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EXAMPLE
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prime(1) = 2 and the greatest k with k! <= 2 is 2, so a(1) = 2.
prime(4) = 7 and the greatest k with k! <= 7 is 3, so a(4) = 3.
prime(10) = 29 and the greatest k with k! <= 29 is 4 so a(10) = 4.
Rows with n, prime(n), greatest k! <=n, a(n) for n = 1..14
n 1 2 3 4 5 6 7 8 9 10 11 12 13 14
prime(n) 2 3 5 7 11 13 17 19 23 29 31 37 41 43
greatest k! 2 2 2 6 6 6 6 6 6 24 24 24 24 24
a(n) 2 2 2 3 3 3 3 3 3 4 4 4 4 4
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PROG
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(PARI) a(n) = my(k=1); until (k! > prime(n), k++); k-1; \\ Michel Marcus, Jul 19 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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