A270446 - OEIS

%I #14 Sep 08 2022 08:46:16

%S 906,3342,3432,4152,4812,4842,5730,7388,7812,8922,10236,10512,11082,

%T 11436,12372,12732,13092,14022,14142,14382,14532,15042,15120,16026,

%U 16866,17370,18210,18612,18896,18898,20142,20322,20382,20652,21672,24132,24432,24462

%N Positive even numbers which are neither of the form p + 2^m + 1 nor of the form p + 2^m - 1 with p prime.

%C Numbers whose distance to both nearest neighbor de Polignac numbers is 1.

%H Robert Israel, <a href="/A270446/b270446.txt">Table of n, a(n) for n = 1..10000</a>

%p filter:= proc(n) local m;

%p    for m from 1 while n - 2^m > 0 do

%p      if isprime(n - 2^m + 1) or isprime(n - 2^m-1) then return false fi

%p    od;

%p    true

%p end proc:

%p select(filter, [seq(i,i=4..30000,2)]); # _Robert Israel_, Mar 22 2016

%o (Magma) lst:=[]; for n in [2..24462 by 2] do t:=Floor(Log(2, n)); c:=0; m:=0; while m le t do a:=n-2^m; if IsPrime(a+1) or IsPrime(a-1) then break; end if; c+:=1; m+:=1; end while; if c eq t+1 then Append(~lst, n); end if; end for; lst;

%Y Cf. A006285.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Mar 17 2016