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%I #15 Jul 18 2019 07:45:50
%S 3,7,2,31,2,127,2,3,2,2047,2,8191,2,3,2,131071,2,524287,2,3,2,8388607,
%T 2,5,2,3,2,536870911,2,2147483647,2,3,2,5,2,137438953471,2,3,2,
%U 2199023255551,2,8796093022207,2,3,2,140737488355327,2,7,2,3,2,9007199254740991
%N a(n) = A000225(n) if n is prime, a(n) = A020639(n) otherwise.
%C What is the asymptotic behavior of the sequences defined by the recursive map x -> a(x)? Do these sequences increase without bound or do they enter a repeating cycle?
%C For example, the trajectory of 11 under the above map starts 11, 2047, 23, 8388607, 47, 140737488355327, 2351, s, 4703, t, ..., where s is a 708-digit number and t is a 1416-digit number. t has no prime factor less than 2^64 (cf. GIMPS link).
%H GIMPS, <a href="https://www.mersenne.org/report_exponent/?exp_lo=4703&exp_hi=&full=1">PrimeNet Exponent Status for M4703</a>
%o (PARI) a(n) = if(ispseudoprime(n), 2^n-1, factor(n)[1, 1])
%Y Cf. A000225, A006370, A020639.
%K nonn
%O 2,1
%A _Felix Fröhlich_, May 30 2019
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