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A276458 Smallest odd number not of the form p + 2^k with p prime and k >= 0 that is divisible by the n-th prime.

%I A276458 #14 Sep 08 2022 08:46:17
%S A276458 1719,905,959,1199,1807,1207,2983,1541,2465,1271,5143,1271,2279,1927,
%T A276458 2279,1829,5917,1541,1207,2263,3239,7387,4717,1649,6161,4841,7169,
%U A276458 1199,1243,127,10873,959,1529,149,11023,2669,12877,2171,1211,1969,905,1719,7913,7289
%N A276458 Smallest odd number not of the form p + 2^k with p prime and k >= 0 that is divisible by the n-th prime.
%C A276458 a(n) <= A213529(n).
%H A276458 Robert Israel, <a href="/A276458/b276458.txt">Table of n, a(n) for n = 2..3000</a>
%e A276458 a(3) = 905 because it is the smallest de Polignac number (A006285) divisible by the third prime.
%p A276458 N:= 10^5: # to use de Polignac numbers <= N
%p A276458 P:= select(isprime,{2,seq(i,i=3..N,2)}):
%p A276458 dP:= {seq(i,i=1..N,2)}:
%p A276458 for k from 0 to ilog2(N) do
%p A276458   dP:= dP minus map(`+`,P,2^k)
%p A276458 od:
%p A276458 for m from 2 do
%p A276458    R:= ListTools:-SelectFirst(1, t -> t mod P[m] = 0, dP);
%p A276458    if R = {} then break fi;
%p A276458    A[m]:= R[1];
%p A276458 od:
%p A276458 seq(A[i],i=2..m-1); # _Robert Israel_, Sep 06 2016
%o A276458 (Magma) lst:=[]; for r in [2..45] do p:=NthPrime(r); n:=-p; f:=0; while IsZero(f) do n:=n+2*p; k:=-1; repeat k+:=1; a:=n-2^k; until a lt 1 or IsPrime(a); if a lt 1 then Append(~lst, n); f:=1; end if; end while; end for; lst;
%Y A276458 Cf. A006285, A098237, A213529.
%K A276458 nonn
%O A276458 2,1
%A A276458 _Arkadiusz Wesolowski_, Sep 03 2016