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 A338884 The smallest number of bits which need to be appended to the binary representation of n to reach a prime greater than n. 1
 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 3, 1, 2, 1, 3, 2, 1, 2, 3, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 1, 2, 1, 4, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) is also the distance from a node to its first prime-number descendant in a binary tree defined as: root = 1 and, for any node n, the left child = 2*n and right child = 2*n + 1. The number of primes among the nodes of depth m is equal to A036378(m) for m>=2. LINKS FORMULA a(n) = bitlength(A208241(n)) - bitlength(n), where bitlength = A070939. - Kevin Ryde, Nov 13 2020 PROG (Python) from sympy import isprime for n in range(1, 101):     a = 0     k = i = 1     while isprime(i) == 0:         a += 1         k = 2*k         for i in range(k*n + 1, k*n + k):             if isprime(i) == 1: break     print(a) CROSSREFS Cf. A000040, A036378, A208241, A005097 (where a(n)=1). Cf. A108234 (zero or more bits). Sequence in context: A076845 A161906 A319135 * A204901 A016014 A067760 Adjacent sequences:  A338881 A338882 A338883 * A338885 A338886 A338887 KEYWORD nonn AUTHOR Ya-Ping Lu, Nov 13 2020 STATUS approved

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)