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A323075
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The fixed point reached when map x -> 1+(x-(largest divisor d < x)) is iterated, starting from x = n.
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4
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1, 2, 3, 3, 5, 3, 7, 5, 7, 3, 11, 7, 13, 5, 11, 7, 17, 3, 19, 11, 11, 7, 23, 13, 11, 5, 19, 11, 29, 7, 31, 17, 23, 3, 29, 19, 37, 11, 19, 11, 41, 7, 43, 23, 31, 13, 47, 11, 43, 5, 29, 19, 53, 11, 31, 29, 19, 7, 59, 31, 61, 17, 43, 23, 53, 3, 67, 29, 47, 19, 71, 37, 73, 11, 29, 19, 67, 11, 79, 41, 31, 7, 83, 43, 47, 23, 59, 31, 89, 13
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OFFSET
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1,2
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COMMENTS
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After a(1) = 1, the fixed point reached is always a prime. Question: Do all odd primes occur infinitely often?
Yes. All odd primes occur infinitely often. A060681(2*k) = k + 1 and so for each k > 1 there exists an integer m such that a(m) = p where p is an odd prime. - David A. Corneth, Jan 07 2019
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LINKS
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FORMULA
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If n == (1+A060681(n)), then a(n) = n, otherwise a(n) = a(1+A060681(n)).
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MATHEMATICA
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{1}~Join~Array[FixedPoint[1 + (# - Divisors[#][[-2]]) &, #] &, 89, 2] (* Michael De Vlieger, Jan 04 2019 *)
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PROG
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(PARI)
A060681(n) = (n-if(1==n, n, n/vecmin(factor(n)[, 1])));
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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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