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
Keywords
Examples
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.
Programs
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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
Comments