A039634 Fixed point of "n -> n/2 or (n-1)/2 until result is prime".

1, 2, 3, 2, 5, 3, 7, 2, 2, 5, 11, 3, 13, 7, 7, 2, 17, 2, 19, 5, 5, 11, 23, 3, 3, 13, 13, 7, 29, 7, 31, 2, 2, 17, 17, 2, 37, 19, 19, 5, 41, 5, 43, 11, 11, 23, 47, 3, 3, 3, 3, 13, 53, 13, 13, 7, 7, 29, 59, 7, 61, 31, 31, 2, 2, 2, 67, 17, 17, 17, 71, 2, 73, 37, 37, 19, 19, 19, 79, 5, 5

Offset

1,2

Comments

a(n) is the largest prime whose binary expansion is an initial substring of n's binary expansion. - Charlie Neder, Oct 27 2018

a(1) = 1 by convention. - David A. Corneth, Oct 27 2018

Links

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

Mathematica

ner[ n_Integer ] := FixedPoint[ If[ EvenQ[ # ]&&#>2, #/2, If[ PrimeQ[ # ]||(#=== 1), #, (#-1)/2 ] ]&, n, 20 ]

Prog

(Haskell)
a039634 1 = 1
a039634 n = until ((== 1) . a010051) (flip div 2) n
-- Reinhard Zumkeller, Nov 17 2013
(PARI) a(n)=while(n>3 && !isprime(n), n\=2); n \\ Charles R Greathouse IV, Jun 23 2017
(Python)
from sympy import isprime
def a(n):
    while n>1 and not isprime(n): n>>=1
    return n
print([a(n) for n in range(1, 82)]) # Michael S. Branicky, Jul 24 2023

Crossrefs

Cf. A039635-A039645, A010051, A039636, A039638, A039639.

Sequence in context: A130088 A369033 A078834 * A078833 A210437 A109674

Adjacent sequences: A039631 A039632 A039633 * A039635 A039636 A039637

Keyword

nonn,easy,nice

Author

Wouter Meeussen

Extensions

Offset corrected by Reinhard Zumkeller, Nov 17 2013

Status

approved