A292936 - OEIS

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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.

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

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OFFSET

1,5

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

FORMULA

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

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

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

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 *)

PROG

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

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

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).

Sequence in context: A029833 A050948 A282695 * A062590 A139215 A139216

Adjacent sequences: A292933 A292934 A292935 * A292937 A292938 A292939

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 27 2017

STATUS

approved