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

Author

Leroy Quet, Dec 04 2008

Keywords

• nonn

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

Crossrefs

Cf. A023758.

Programs

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 *)

Extensions

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