login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117406 Integer k such that 2^n + k = A117405(n). 5
3, 2, 0, 1, -1, 1, 1, 1, -2, -1, 3, -1, 1, 1, -2, -3, -5, 1, -2, 1, 1, -3, 7, -1, 3, -3, 3, 3, 1, 6, -3, 1, 1, -3, -3, -3, -3, -1, 18, 3, 1, -1, 3, 1, -3, 3, 7, -9, 3, -1, 7, -5, 3, 11, -3, -5, 6, -9, -3, -1, -3, 1, -2, 9, 1, 5, 3, -1, -5, -13, 9, -3, -7, -3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

After n=2, never again is a(n) = 0. Semiprime analog of A117388 Integer k such that 2^n + k = A117387(n). A117387(n) is prime nearest to 2^n. (In case of a tie, choose the smaller).

LINKS

Table of n, a(n) for n=0..73.

FORMULA

a(n) = A117405(n) - 2^n. a(n) = Min{k such that A001358(i) + k = 2^j}.

EXAMPLE

a(0) = 3 because 2^0 + 3 = 4 = A001358(1) and no semiprime is closer to 2^0.

a(1) = 2 because 2^1 + 2 = 4 = A001358(1) and no semiprime is closer to 2^1.

a(2) = 0 because 2^2 + 0 = 4 = A001358(1) and no semiprime is closer to 2^2.

a(3) = 1 because 2^3 + 1 = 9 = 3^2 = A001358(3), no semiprime is closer to 2^3.

a(4) = -1 because 2^4 - 1 = 15 = 3 * 5 and no semiprime is closer.

a(5) = 1 because 2^5 + 1 = 33 = 3 * 11 and no semiprime is closer to 2^5.

a(6) = 1 because 2^6 + 1 = 65 = 5 * 13 and no semiprime is closer to 2^6.

a(7) = 1 because 2^7 + 1 = 129 = 3 * 43 and no semiprime is closer to 2^7.

a(8) = -2 because 2^8 - 2 = 254 = 2 * 127 and no semiprime is closer to 2^8.

MATHEMATICA

a[n_] := Catch@Block[{p = 2^n, k = 0}, While[True, If[p > k && PrimeOmega[p - k] == 2, Throw[-k]]; If[PrimeOmega[p + k] == 2, Throw[k]]; k++]]; a /@ Range[0, 80] a /@ Range[0, 80] (* Giovanni Resta, Jun 15 2016 *)

CROSSREFS

Cf. A000079, A001358, A117387, A117405.

Sequence in context: A131290 A138741 A116604 * A290216 A293202 A280265

Adjacent sequences:  A117403 A117404 A117405 * A117407 A117408 A117409

KEYWORD

easy,sign,less

AUTHOR

Jonathan Vos Post, Mar 13 2006

EXTENSIONS

Corrected and extended by Giovanni Resta, Jun 15 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 14 00:21 EST 2017. Contains 295976 sequences.