A232084 - OEIS

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A232084

Least k such that prime(n) + 2^(k+L) - 2^L is a prime, where L is the length of binary representation of prime(n): L = A070939(A000040(n)). a(n) = -1 if no such k exists.

1, 1, 2, 2, 1, 2, 4, 4, 1, 2, 1, 2, 1, 2, 4, 2, 3, 4, 1, 2, 2, 1, 5, 4, 1, 2, 2, 4, 1, 6, 18, 20, 2, 4, 2, 3, 1, 4, 2, 2, 3, 6, 1, 12, 2, 1, 1, 96, 2, 4, 4, 2, 2, 1, 3, 3, 4, 6, 6, 4, 3, 6, 1, 4, 1, 2, 2, 1, 56, 2, 3, 8, 4, 4, 3, 4, 2, 4, 4, 3, 4, 4, 18, 20, 2, 8, 2, 2

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OFFSET

2,3

COMMENTS

Least number of 1's that must be prepended to the binary representation of prime(n) such that the result is another prime.

Prime(n) is in A065047 if and only if a(n) = 1.

LINKS

Table of n, a(n) for n=2..89.

EXAMPLE

a(6) = 1 because 13 in binary is 1101, and 29 (11101 in binary) is a prime.

a(7) = 2 because 17 in binary is 10001, and 113 (1110001 in binary) is a prime.

a(8) = 4 because 19 in binary is 10011, and 499 (111110011 in binary) is a prime.