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A117417
Integer k such that 3^n + k = A117416(n).
0
3, 1, 0, -1, 1, 4, 2, -1, -2, -4, -2, 2, -2, -1, 10, -2, 1, -4, 4, -2, -2, -2, -12, -4, 8, -2, -7, 2, -2, 8, 14, -5, 1, -4, -8, -4, 16, 6, -6, -2, 2, -8, -2, 12, -2, -5, -8, 10, -2, 4, -10, 40, 8, -10, 4, -2, -34, -2, 4, -20, -2
OFFSET
0,1
COMMENTS
Distance from 3^n to the nearest semiprime. If there are two semiprimes at the same distance, take the negative k-value.
See also: A117405 Semiprime nearest to 2^n. A117387 Prime nearest to 2^n.
FORMULA
a(n) = Integer k such that 3^n + k = A117416(n). a(n) = A117416(n) - 3^n. a(n) = Min{k such that A001358(i) + k = 3^n}.
EXAMPLE
a(0) = 3 because 3^0 + 3 = 4 = A001358(1) and no semiprime is closer to 3^0.
a(1) = 1 because 3^1 + 1 = 4 = A001358(1) and no semiprime is closer to 3^1.
a(2) = 0 because 3^2 + 0 = 9 = 3^2 = A001358(3), no semiprime is closer to 3^2 [this is the only 0 element].
a(3) = -1 because 3^3 - 1 = 26 = 2 * 13, no semiprime is closer.
a(4) = 1 because 3^4 + 1 = 82 = 2 * 41, no semiprime is closer.
a(5) = 4 because 3^5 + 4 = 247 = 13 * 19, no semiprime is closer.
CROSSREFS
KEYWORD
easy,sign,less
AUTHOR
Jonathan Vos Post, Mar 13 2006
STATUS
approved