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

2, 328, 562, 716, 794, 898, 1084, 1772, 1808, 1918, 1924, 1972, 2186, 2434, 2564, 2572, 2894, 2986, 3056, 3524, 3578, 3716, 3868, 4144, 4304, 4414, 4714, 4774, 4838, 4852, 4924, 5072, 5098, 5164, 5204, 5272, 5338, 5398, 5456, 5614, 5708, 5756, 5968, 5972, 5974

Offset: 1

Author

Arkadiusz Wesolowski, Feb 15 2017

Keywords

• nonn
• easy

Comments

Sequence is infinite, since any integer congruent to 63064644938 modulo 195435717998430 cannot be the sum of a power of three and a prime.

A282432(a(n)) = 0.

Examples

			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.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A282432.

Intersection of A001651 and A058517. - Michel Marcus, Feb 25 2017

Programs

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;

Mathematica

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 *)

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