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%I #24 Jan 19 2019 03:45:56
%S 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,
%T 29,7,31,17,23,3,29,19,37,11,19,11,41,7,43,23,31,13,47,11,43,5,29,19,
%U 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
%N The fixed point reached when map x -> 1+(x-(largest divisor d < x)) is iterated, starting from x = n.
%C After a(1) = 1, the fixed point reached is always a prime. Question: Do all odd primes occur infinitely often?
%C 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
%H Antti Karttunen, <a href="/A323075/b323075.txt">Table of n, a(n) for n = 1..20669</a>
%F If n == (1+A060681(n)), then a(n) = n, otherwise a(n) = a(1+A060681(n)).
%F a(2^k * p - 2^(k+1) + 2) = a(A000079(k) * p - A000918(k+1)) = p for k >= 0. - _David A. Corneth_, Jan 08 2019
%F a(1) = 1, and for n > 1, a(n) = A000040(A323164(n)). - _Antti Karttunen_, Jan 08 2019
%t {1}~Join~Array[FixedPoint[1 + (# - Divisors[#][[-2]]) &, #] &, 89, 2] (* _Michael De Vlieger_, Jan 04 2019 *)
%o (PARI)
%o A060681(n) = (n-if(1==n,n,n/vecmin(factor(n)[,1])));
%o A323075(n) = { my(nn = 1+A060681(n)); if(nn==n,n,A323075(nn)); };
%Y Cf. A000040, A000079, A000918, A060681, A323076, A323079, A323164, A323165 (ordinal transform).
%Y Cf. also A039650, A039654.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jan 04 2019
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