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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.

%I A292936 #40 Oct 01 2017 00:28:49
%S A292936 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 A292936 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 A292936 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 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.
%C A292936 Records occur at positions 1, 2, 5, 11, 23, 47, 2879, ... (A292937).
%H A292936 Antti Karttunen, <a href="/A292936/b292936.txt">Table of n, a(n) for n = 1..65537</a>
%F A292936 a(n) = A007814(1+A292599(n)).
%F A292936 For n >= 1, a(n) <= A078349(n).
%F A292936 For n > 47, a(n) <= A007814(1+n).
%p A292936 A292936 := proc(n)
%p A292936     for k from 0 do
%p A292936         if not isprime(floor(n/2^k)) then
%p A292936             return k;
%p A292936         end if;
%p A292936     end do:
%p A292936 end proc:
%p A292936 seq(A292936(n),n=1..100) ; # _R. J. Mathar_, Sep 28 2017
%t A292936 Table[SelectFirst[Range[0, 10], ! PrimeQ@ Floor[n/(2^#)] &], {n, 105}] (* _Michael De Vlieger_, Sep 29 2017 *)
%o A292936 (PARI) A292936(n) = { my(k=0); while(isprime(n), n >>= 1; k++); k; };
%o A292936 (Scheme) (define (A292936 n) (A007814 (1+ (A292599 n))))
%Y A292936 Cf. A007814, A078349, A292599, A292937.
%Y A292936 Cf. A000040, A005385, A066179, A157358, A157359 (positions of terms that are > k, for k = 0..4).
%Y A292936 Cf. A059456 (positions of ones).
%K A292936 nonn
%O A292936 1,5
%A A292936 _Antti Karttunen_, Sep 27 2017