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%I #23 Sep 08 2022 08:45:25
%S 1,2,16,22,26,28,36,40,46,50,52,56,58,64,70,76,78,82,86,88,92,94,96,
%T 100,106,112,116,118,120,122,124,126,127,134,136,142,144,146,148,149,
%U 154,156,160,162,166,170,172,176,178,184,186,188,190,196,202,204,206,208
%N Numbers that cannot be written as 2^k + prime.
%C A109925(a(n)) = 0.
%H Reinhard Zumkeller, <a href="/A118954/b118954.txt">Table of n, a(n) for n = 1..10000</a>
%H 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 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 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 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 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 (Haskell)
%o a118954 n = a118954_list !! (n-1)
%o a118954_list = filter f [1..] where
%o f x = all (== 0) $ map (a010051 . (x -)) $ takeWhile (< x) a000079_list
%o -- _Reinhard Zumkeller_, Jan 03 2014
%o (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 (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 Complement of A118955. Subsequence of A118956. Supersequence of A006285.
%Y Cf. A156695, A010051, A000079.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, May 07 2006
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