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A282430 Even numbers not divisible by 3 which are not of the form p + 3^x with p prime.

%I A282430 #17 Sep 08 2022 08:46:18
%S A282430 2,328,562,716,794,898,1084,1772,1808,1918,1924,1972,2186,2434,2564,
%T A282430 2572,2894,2986,3056,3524,3578,3716,3868,4144,4304,4414,4714,4774,
%U A282430 4838,4852,4924,5072,5098,5164,5204,5272,5338,5398,5456,5614,5708,5756,5968,5972,5974
%N A282430 Even numbers not divisible by 3 which are not of the form p + 3^x with p prime.
%C A282430 Sequence is infinite, since any integer congruent to 63064644938 modulo 195435717998430 cannot be the sum of a power of three and a prime.
%C A282430 A282432(a(n)) = 0.
%H A282430 Robert G. Wilson v, <a href="/A282430/b282430.txt">Table of n, a(n) for n = 1..1000</a>
%e A282430 328 is in the sequence since 328 - 3^0 = 3*109, 328 - 3^1 = 5^2*13, 328 - 3^2 = 11*29, 328 - 3^3 = 7*43, 328 - 3^4 = 13*19, and 328 - 3^5 = 5*17 are all composite.
%t A282430 fQ[n_] := If[ Mod[n, 3] > 0, Block[{lmt = Log[3, n], x = 0}, While[x < lmt && !PrimeQ[n - 3^x], x++]; x > lmt], False]; Select[ 2Range@3000, fQ] (* _Robert G. Wilson v_, Feb 25 2017 *)
%o A282430 (Magma) lst:=[]; for n in [0..5974 by 2] do if not n mod 3 eq 0 then x:=-1; repeat x+:=1; p:=n-3^x; until p lt 2 or IsPrime(p); if p lt 2 then Append(~lst, n); end if; end if; end for; lst;
%o A282430 (PARI) isok(n) = {if (n % 2, 0, if (n % 3, lim = log(n)/log(3); for (k=0, lim, if (isprime(n - 3^k), return (0));); 1, 0););} \\ _Michel Marcus_, Feb 25 2017
%Y A282430 Cf. A282432.
%Y A282430 Intersection of A001651 and A058517. - _Michel Marcus_, Feb 25 2017
%K A282430 nonn,easy
%O A282430 1,1
%A A282430 _Arkadiusz Wesolowski_, Feb 15 2017