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A257729
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Permutation of natural numbers: a(1)=1; a(prime(n)) = oddprime(a(n)), a(composite(n)) = not_an_oddprime(1+a(n)).
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4
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1, 3, 7, 2, 19, 6, 5, 12, 4, 28, 71, 10, 17, 9, 20, 8, 13, 40, 41, 95, 16, 26, 11, 15, 30, 14, 21, 56, 109, 57, 359, 125, 25, 38, 18, 24, 31, 44, 22, 32, 61, 77, 29, 143, 78, 445, 73, 162, 36, 54, 27, 35, 23, 45, 62, 33, 46, 84, 43, 104, 179, 42, 185, 105, 545, 98, 181, 208, 51, 75, 503, 39, 59, 50, 34, 63, 85, 48, 103, 64, 114, 60, 37
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OFFSET
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1,2
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COMMENTS
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Here composite(n) = n-th composite = A002808(n), prime(n) = n-th prime = A000040(n), oddprime(n) = n-th odd prime = A065091(n) = A000040(n+1), not_an_oddprime(n) = n-th natural number which is not an odd prime = A065090(n).
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LINKS
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FORMULA
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As a composition of other permutations:
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EXAMPLE
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As an initial value we have a(1) = 1.
2 is the first prime (= A000040(1)), so we take the a(1)-th odd prime, A065091(1) = 3, thus a(2) = 3.
3 is the second prime, thus we take a(2)-th odd prime, A065091(3) = 7, thus a(3) = 7.
4 is the first composite, thus we take a(1)-th number larger than one which is not an odd prime, and that is A065090(1+1) = 2, thus a(4) = 2.
5 is the third prime, thus we take a(3)-th odd prime, which is A065091(7) = 19, thus a(5) = 19.
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PROG
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(PARI)
A002808(n) = { my(k=-1); while( -n + n += -k + k=primepi(n), ); n};
for(n=1, 10000, write("b257729.txt", n, " ", A257729(n)));
(Scheme, with memoizing definec-macro)
;; Alternatively, by composing other permutations:
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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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