cp's OEIS Frontend

A294659 Largest number in the orbit of n under iteration of the map A293975: x -> x/2 if even, x + nextprime(x) else.

%I A294659 #5 Nov 08 2017 12:27:37
%S A294659 0,8,8,8,12,8,20,8,20,12,24,12,32,20,32,16,36,20,44,20,44,24,52,24,56,
%T A294659 32,56,28,60,32,68,32,72,36,72,36,80,44,80,40,84,44,92,44,92,52,100,
%U A294659 48,104,56,104,52,112,56,116,56,116,60,120,60,128,68,132,64,132,72,140,68,140,72,144,72,152,80
%N A294659 Largest number in the orbit of n under iteration of the map A293975: x -> x/2 if even, x + nextprime(x) else.
%C A294659 The trajectory under iterations of A293975 seems to end in the cycle 1 -> 3 -> 8 -> 4 -> 2 -> 1, for any positive starting value n. Therefore a(n) >= 8 for all n > 0.
%C A294659 Obviously also a(n) >= n for all numbers, with equality for powers of two 2^k with k >= 3; a(n) >= n + nextprime(n) >= 2n+2 for all odd numbers.
%C A294659 Record values not of the form f(n) = n + nextprime(n) occur for a(1) = 8, a(5) = 12, a(7) = 20, a(11) = 24, a(13) = 32, a(17) = 36, a(19) = 44, a(23) = 52, a(25) = 56, a(29) = 60, a(31) = 68, a(33) = 72, a(37) = 80, a(41) = 84, a(43) = 92, a(47) = 100, ... We see that in most cases, this equals f(f(n)/2). Exceptions are n = 1, 7, 13, 19, 37, 43, 67, 79, 89, 97, ...
%o A294659 (PARI) A294659(n,S=[n])={while(#S<#S=setunion(S,[n=A293975(n)]),); vecmax(S)}
%Y A294659 Cf. A293975, A293982 (size of the orbit).
%K A294659 nonn
%O A294659 0,2
%A A294659 _M. F. Hasler_, Nov 06 2017