A152449 Primes of the form 2^j - 2^k + 1, where j > k >= 0.

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

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

Ivan Neretin, Table of n, a(n) for n = 1..1000

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

Adjacent sequences: A152446 A152447 A152448 * A152450 A152451 A152452

Keyword

nonn

Author

Leroy Quet, Dec 04 2008

Extensions

Extended by R. J. Mathar, Stefan Steinerberger and Ray Chandler, Dec 05 2008

Status

approved