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A152449
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Primes of the form 2^j - 2^k + 1, where j > k >= 0.
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0
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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; internal format)
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OFFSET
| 1,1
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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.
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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: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2008]
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CROSSREFS
| A023758
Sequence in context: A094947 A092621 A188809 * A048975 A009571 A087520
Adjacent sequences: A152446 A152447 A152448 * A152450 A152451 A152452
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Dec 04 2008
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EXTENSIONS
| Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 05 2008
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