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A373063
Greatest k >= 1 such that (p + 1 - 2^i) / 2^i is prime for i = 1..k and p is prime from A005385.
0
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.
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
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, May 21 2024
STATUS
approved