A117417 Integer k such that 3^n + k = A117416(n).

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.

Links

Table of n, a(n) for n=0..60.

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

Cf. A000079, A001358, A117387, A117405, A117406, A117416.

Sequence in context: A305161 A250484 A294250 * A231345 A271344 A327622

Adjacent sequences: A117414 A117415 A117416 * A117418 A117419 A117420

Keyword

easy,sign,less

Author

Jonathan Vos Post, Mar 13 2006

Status

approved