cp's OEIS Frontend

A118954 Numbers that cannot be written as 2^k + prime.

%I A118954 #23 Sep 08 2022 08:45:25
%S A118954 1,2,16,22,26,28,36,40,46,50,52,56,58,64,70,76,78,82,86,88,92,94,96,
%T A118954 100,106,112,116,118,120,122,124,126,127,134,136,142,144,146,148,149,
%U A118954 154,156,160,162,166,170,172,176,178,184,186,188,190,196,202,204,206,208
%N A118954 Numbers that cannot be written as 2^k + prime.
%C A118954 A109925(a(n)) = 0.
%H A118954 Reinhard Zumkeller, <a href="/A118954/b118954.txt">Table of n, a(n) for n = 1..10000</a>
%H A118954 Roger Crocker, <a href="http://www.jstor.org/stable/2688349">A theorem concerning prime numbers</a>, Mathematics Magazine 34:6 (1961), pp. 316+344.
%H A118954 P. Erdős, <a href="http://www.renyi.hu/~p_erdos/1950-07.pdf">On integers of the form 2^k + p and some related problems</a>, Summa Brasil. Math. 2 (1950), 113-123.
%H A118954 N. P. Romanoff, <a href="http://resolver.sub.uni-goettingen.de/purl?GDZPPN002276984">Über einige Sätze der additiven Zahlentheorie</a>, Math. Ann. 57 (1934), pp. 668-678.
%H A118954 J. G. van der Corput, On de Polignac’s conjecture, Simon Stevin 27 (1950), pp. 99-105. Cited in <a href="http://www.ams.org/mathscinet-getitem?mr=35298">MR 35298</a>.
%F A118954 n < a(n) < kn for some k < 2 and all large enough n, see Romanoff and either Erdős or van der Corput. - _Charles R Greathouse IV_, Sep 01 2015
%o A118954 (Haskell)
%o A118954 a118954 n = a118954_list !! (n-1)
%o A118954 a118954_list = filter f [1..] where
%o A118954    f x = all (== 0) $ map (a010051 . (x -)) $ takeWhile (< x) a000079_list
%o A118954 -- _Reinhard Zumkeller_, Jan 03 2014
%o A118954 (PARI) is(n)=my(k=1);while(k<n,if(isprime(n-k),return(0));k*=2);1 \\ _Charles R Greathouse IV_, Sep 01 2015
%o A118954 (Magma) lst:=[]; for n in [1..208] do k:=-1; repeat k+:=1; a:=n-2^k; until a lt 1 or IsPrime(a); if a lt 1 then Append(~lst, n); end if; end for; lst; // _Arkadiusz Wesolowski_, Sep 02 2016
%Y A118954 Complement of A118955. Subsequence of A118956. Supersequence of A006285.
%Y A118954 Cf. A156695, A010051, A000079.
%K A118954 nonn
%O A118954 1,2
%A A118954 _Reinhard Zumkeller_, May 07 2006