login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A057673 Smallest prime p such that |2^n - p| is a prime. 3
3, 5, 2, 3, 3, 3, 3, 19, 5, 3, 3, 19, 3, 13, 3, 19, 17, 13, 5, 19, 3, 19, 3, 37, 3, 61, 5, 79, 89, 3, 41, 19, 5, 79, 41, 31, 5, 31, 107, 7, 167, 31, 11, 67, 17, 139, 167, 127, 59, 139, 71, 139, 47, 379, 53, 67, 5, 13, 137, 607, 107, 31, 167, 409, 59, 79, 5, 19, 23, 19, 71, 577, 107 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The absolute value is relevant only for first two terms, 2^0-a(0) = 1-3 = -2, 2^1-a(1) = 2-5 = -3. According to Goldbach's conjecture, every even number > 2 is the sum of two primes, which implies that for all further terms, a(n) < 2^n. - M. F. Hasler, Jan 13 2011
LINKS
EXAMPLE
n=7, 2^n=128. The smallest terms subtracted from 128 resulting in a prime are 1,15,19,... Neither 1 nor 15 are primes but 19 is a prime. It gives 109=128-19, so a(n)=19.
MATHEMATICA
f[n_] := Block[{p = 2}, While[! PrimeQ[2^n - p], p = NextPrime@ p]; p]; Array[f, 60, 0]
PROG
(PARI) A057673(n)=forprime( p=1, default(primelimit), ispseudoprime(abs(2^n-p))& return(p))
CROSSREFS
Analog of A056206. Cf. A056208, A057662.
Sequence in context: A282574 A076562 A306220 * A279398 A241429 A200109
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 19 2000
EXTENSIONS
Offset corrected and initial term added by M. F. Hasler, Jan 13 2011
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 20 05:30 EDT 2024. Contains 374441 sequences. (Running on oeis4.)