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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. 7

%I

%S 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,

%T 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,

%U 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

%N 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.

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

%H Antti Karttunen, <a href="/A292936/b292936.txt">Table of n, a(n) for n = 1..65537</a>

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

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

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

%p A292936 := proc(n)

%p for k from 0 do

%p if not isprime(floor(n/2^k)) then

%p return k;

%p end if;

%p end do:

%p end proc:

%p seq(A292936(n),n=1..100) ; # _R. J. Mathar_, Sep 28 2017

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

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

%o (Scheme) (define (A292936 n) (A007814 (1+ (A292599 n))))

%Y Cf. A007814, A078349, A292599, A292937.

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

%Y Cf. A059456 (positions of ones).

%K nonn

%O 1,5

%A _Antti Karttunen_, Sep 27 2017

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Last modified July 15 04:00 EDT 2020. Contains 335762 sequences. (Running on oeis4.)