A292936 a(n) = the least k >= 0 such that floor(n/(2^k)) is a nonprime; a(n) is degree of the "safeness" of prime, 0 if n is not a prime, 1 for unsafe primes (A059456), and k >= 2 for primes that are (k-1)-safe but not k-safe.

0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0

Offset: 1

Author

Antti Karttunen, Sep 27 2017

Keywords

• nonn

Comments

Records occur at positions 1, 2, 5, 11, 23, 47, 2879, ... (A292937).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A007814, A078349, A292599, A292937.

Cf. A000040, A005385, A066179, A157358, A157359 (positions of terms that are > k, for k = 0..4).

Cf. A059456 (positions of ones).

Programs

Maple

A292936 := proc(n)
    for k from 0 do
        if not isprime(floor(n/2^k)) then
            return k;
        end if;
    end do:
end proc:
seq(A292936(n),n=1..100) ; # R. J. Mathar, Sep 28 2017

Mathematica

Table[SelectFirst[Range[0, 10], ! PrimeQ@ Floor[n/(2^#)] &], {n, 105}] (* Michael De Vlieger, Sep 29 2017 *)

PARI

A292936(n) = { my(k=0); while(isprime(n), n >>= 1; k++); k; };

Scheme

(define (A292936 n) (A007814 (1+ (A292599 n))))

Formula

a(n) = A007814(1+A292599(n)).

For n >= 1, a(n) <= A078349(n).

For n > 47, a(n) <= A007814(1+n).