A039645 Number of steps to fixed point of "k -> k/2 or (k+1)/2 until result is prime", starting with prime(n)+1.

1, 2, 2, 3, 3, 2, 3, 3, 4, 5, 5, 2, 3, 3, 5, 4, 6, 2, 3, 5, 2, 5, 4, 3, 4, 4, 4, 5, 5, 3, 7, 4, 6, 6, 4, 4, 2, 3, 5, 5, 4, 4, 7, 2, 5, 5, 3, 6, 4, 4, 3, 8, 3, 8, 5, 5, 5, 5, 2, 3, 3, 4, 7, 7, 2, 7, 3, 4, 6, 6, 3, 5, 5, 4, 8, 8, 6, 2, 3, 3, 4, 2, 7, 3, 7, 7, 3, 2, 5, 5, 4, 9, 4, 5, 9, 9, 9, 3, 3, 2, 3, 8

Offset: 1

Author

Wouter Meeussen

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A039634-A039644.

Cf. A010051, A000040, A039641, A039643, A039637.

Programs

Haskell

a039645 n = snd $ until ((== 1) . a010051 . fst)
            (\(x, i) -> ((x + 1) `div` 2 , i + 1)) (a000040 n + 1, 1)
-- Reinhard Zumkeller, Nov 17 2013

Mathematica

f[k_] := Which[PrimeQ[k], k, EvenQ[k], k/2, True, (k+1)/2];
a[n_] := Length[FixedPointList[f, Prime[n] + 1]] - 1;
Array[a, 102] (* Jean-François Alcover, Mar 01 2019 *)

Extensions

Offset corrected by Reinhard Zumkeller, Nov 17 2013