A335912 Numbers k for which A335885(k) = 2.

9, 11, 13, 15, 18, 19, 21, 22, 23, 25, 26, 29, 30, 35, 36, 38, 41, 42, 44, 46, 47, 49, 50, 51, 52, 58, 60, 61, 67, 70, 72, 76, 79, 82, 84, 85, 88, 92, 93, 94, 97, 98, 100, 102, 104, 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

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..73.

Example

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.
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.

Prog

(PARI)
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))))); };
isA335912(n) = (2==A335885(n));

Crossrefs

Row 2 of A335910.

Cf. A000265, A335911, A335885.

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

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

Sequence in context: A334688 A248629 A008558 * A123760 A289686 A251394

Adjacent sequences: A335909 A335910 A335911 * A335913 A335914 A335915

Keyword

nonn

Author

Antti Karttunen, Jun 30 2020

Status

approved