login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers k for which A335885(k) = 2.
5

%I #25 Jul 09 2020 22:38:40

%S 9,11,13,15,18,19,21,22,23,25,26,29,30,35,36,38,41,42,44,46,47,49,50,

%T 51,52,58,60,61,67,70,72,76,79,82,84,85,88,92,93,94,97,98,100,102,104,

%U 113,116,119,120,122,134,137,140,144,152,155,158,164,168,170,176,184,186,188,191,193,194,196,200,204,208,217,223

%N Numbers k for which A335885(k) = 2.

%C Numbers n such that when we start from k = n, and apply in some combination the nondeterministic maps k -> k - k/p and k -> k + k/p, (where p can be any of the odd prime factors of k), then for some combination we can reach a power of 2 in exactly two steps (but with no combination allowing 0 or 1 steps).

%e For n = 70 = 2*5*7, if we first take p = 7 and apply the map n -> n + (n/p), we obtain 80 = 2^4 * 5. We then take p = 5, and apply the map n -> n - (n/p), to obtain 80-16 = 64 = 2^16. Thus we reached a power of 2 in two steps (and there are no shorter paths), therefore 70 is present in this sequence.

%e For n = 769, which is a prime, 769 - (769/769) yields 768 = 3 * 256. For 768 we can then apply either map to obtain a power of 2, as 768 - (768/3) = 512 = 2^9 and 768 + (768/3) = 1024 = 2^10. On the other hand, 769 + (769/769) = 770 and A335885(770) = 4, so that route would not lead to any shorter paths, therefore 769 is a term of this sequence.

%o (PARI)

%o A335885(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+min(A335885(f[k,1]-1),A335885(f[k,1]+1))))); };

%o isA335912(n) = (2==A335885(n));

%Y Row 2 of A335910.

%Y Cf. A000265, A335911, A335885.

%Y Subsequences of semiprimes (union gives all odd semiprimes present): A144482, A333788, A336115.

%Y Cf. also A334092, A335874, A336116, A336117 and A334102, A335882, A336122.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jun 30 2020