A335878 Numbers k such that A329697(k) = A331410(k).

1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 16, 18, 19, 22, 24, 26, 27, 32, 33, 35, 36, 38, 39, 44, 48, 52, 54, 57, 59, 64, 66, 67, 70, 72, 76, 78, 81, 83, 88, 96, 99, 103, 104, 105, 107, 108, 114, 115, 117, 118, 121, 128, 131, 132, 134, 140, 143, 144, 151, 152, 156, 157, 162, 166, 169, 171, 176, 177, 181, 192, 197, 198, 199, 201, 203, 206

Offset: 1

Author

Antti Karttunen, Jun 29 2020

Keywords

• nonn

Comments

Numbers k such that the number of steps needed to reach a power of 2 when starting at n and iterating with the nondeterministic map k -> k + k/p, is equal to the number of steps needed to reach a power of 2 when starting from the same n and iterating with the map k -> k - k/p, where in both maps, p can be any odd prime factor of k (for example, the largest).

If x and y are included in this sequence, then x*y is also a term.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A329697, A331410.

Positions of zeros in A335877.

Programs

PARI

A329697(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A329697(f[k,1]-1)))); };
A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };
isA335878(n) = (A329697(n)==A331410(n));