A074313 a(n) = the maximal length of a sequence of primes {s_1 = prime(n), s_2 = f(s1), s_3 = f(s_2), ....} formed by repeated application of f(m) = Floor(m/2) on prime(n).

1, 1, 2, 2, 3, 1, 1, 1, 4, 1, 1, 1, 1, 1, 5, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1

Offset

1,3

Comments

The smallest value of n such that a(n) = 6 is n = 417.

Links

Table of n, a(n) for n=1..100.

Example

To compute a(9): prime(9) = 23, f(23) = 11, f(11) = 5, f(5) = 2, f(2) = 1, where f(m) = Floor(m/2). Hence the sequence (of length 4) 23, 11, 5, 2 is the sequence of primes of maximal length formed by repeated application of f to prime(9) = 23. Therefore a(9) = 4.

Mathematica

f[n_] := Module[{i}, i = 0; m = n; While[PrimeQ[m], m = Floor[m/2]; i++ ]; i]; Table[f[Prime[i]], {i, 1, 100}]

Crossrefs

Sequence in context: A329311 A308746 A367125 * A367438 A303506 A213194

Adjacent sequences: A074310 A074311 A074312 * A074314 A074315 A074316

Keyword

easy,nonn

Author

Joseph L. Pe, Sep 22 2002

Status

approved