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A152449 Primes of the form 2^j - 2^k + 1, where j > k >= 0. 4
2, 3, 5, 7, 13, 17, 29, 31, 61, 97, 113, 127, 193, 241, 257, 449, 509, 769, 1009, 1021, 2017, 4093, 7681, 7937, 8161, 8191, 12289, 15361, 16369, 16381, 32257, 61441, 64513, 65521, 65537, 114689, 130817, 131009, 131041, 131071, 520193, 523777 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence contains the primes that are each one more than any term of sequence A023758.
In binary these primes are represented, reading left to right, as some number of 1's, followed by some number of 0's (possibly no 0's), followed finally by one 1 as the rightmost digit.
All odd terms p satisfy the property that (p NOR (p-2))=0. - Gary Detlefs, May 03 2019
LINKS
MAPLE
isA000079 := proc(n) local i ; RETURN( add(i, i=convert(n, base, 2)) = 1 ) ; end : isA000225 := proc(n) isA000079(n+1) ; end: A007814 := proc(n) local p2, a, p ; a := 0 ; p2 := ifactors(n)[2] ; for p in p2 do if op(1, p) = 2 then a := op(2, p) ; fi; od; RETURN(a) ; end: isA023758 := proc(n) local ord ; ord := A007814(n) ; RETURN ( isA000225(n/2^ord) ) ; end: isA152449 := proc(n) local ord, np1 ; if isprime(n) then RETURN ( isA023758(n-1) ) ; else false; fi; end: for i from 1 to 100000 do p := ithprime(i) ; if isA152449(p) then printf("%d, ", p) ; fi; od: # R. J. Mathar, Dec 05 2008
MATHEMATICA
Select[Union[Flatten[Table[2^j-2^k+1, {j, 20}, {k, 0, j-1}]]], PrimeQ] (* Harvey P. Dale, Mar 14 2018 *)
CROSSREFS
Cf. A023758.
Sequence in context: A092621 A188809 A350443 * A048975 A009571 A087520
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 04 2008
EXTENSIONS
Extended by R. J. Mathar, Stefan Steinerberger and Ray Chandler, Dec 05 2008
STATUS
approved

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Last modified June 24 00:53 EDT 2024. Contains 373661 sequences. (Running on oeis4.)