A373063 Greatest k >= 1 such that (p + 1 - 2^i) / 2^i is prime for i = 1..k and p is prime from A005385.

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

Offset

1,3

Comments

"k-safe primes" iff (p + 1 - 2^i) / 2^i is prime for i = 0..k, p a prime number. A000040 are 0-safe primes, A005385 are 1-safe primes, A066179 are 2-safe primes.

Links

Table of n, a(n) for n=1..97.

Example

p = 11: (11 + 1 - 2^i) / 2^i is prime for i = 1..2, thus a(3) = 2.
p = 47: (47 + 1 - 2^i) / 2^i is prime for i = 1..4, thus a(5) = 4.

Prog

(PARI) isp(k) = (denominator(k) == 1) && isprime(k);
f(p) = my(i=1); while (isp((p+1-2^i)/2^i), i++); i-1;
apply(f, select(x->isp((x-1)/2), primes(1000))) \\ Michel Marcus, May 28 2024

Crossrefs

Cf. A000040, A005385, A066179.

Sequence in context: A339255 A086198 A086196 * A332937 A350351 A138297

Adjacent sequences: A373060 A373061 A373062 * A373064 A373065 A373066

Keyword

nonn

Author

Ctibor O. Zizka, May 21 2024

Status

approved