

A196698


Number of primes of the form 3^n + 3^k + 1 with 0 <= k < n.


6



2, 4, 6, 8, 7, 11, 7, 10, 11, 11, 8, 10, 9, 11, 14, 11, 10, 14, 7, 16, 12, 12, 7, 17, 10, 7, 15, 13, 4, 11, 11, 11, 13, 6, 12, 18, 9, 12, 17, 14, 13, 11, 10, 11, 13, 6, 7, 17, 9, 14, 9, 10, 13, 20, 8, 11, 10, 9, 8, 16, 12, 12, 13, 8, 12, 14, 8, 8, 10, 13, 9
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OFFSET

1,1


COMMENTS

Conjecture: all elements of this sequence are greater than 0.
Conjecture verified up to n = 7399.
I conjecture the contrary: infinitely many elements of this sequence are equal to 0. Probably the first n with a(n) = 0 is less than a million.  Charles R Greathouse IV, Nov 21 2011
This is also number of primes in ndigit balanced ternary form with no more than three nonzero digits for n > 1.  Lei Zhou, Dec 04 2013


LINKS

Lei Zhou, Table of n, a(n) for n = 1..6205
Lei Zhou, A 400,000 decimal digits balanced ternary prime with three nonzero digits, found on Jan 02 2015.


EXAMPLE

n = 1, 3 = 3^1 + 3^0  1 = 3^1  3^0 + 1; 5 = 3^1 + 3^0 + 1, two primes found, so a(1) = 2;
n = 2, 5 = 3^2  3^1  1; 7 = 3^2  3^1 + 1 = 3^2  3^0  1; 11 = 3^2 + 3^1  1 = 3^2 + 3^0 + 1; 13 = 3^2 + 3^1 + 1, four primes found, so a(2) = 4;
...
n = 7, 1459 = 3^7  3^6 + 1; 2161 = 3^7  3^3 + 1; 2179 = 3^7  3^1 + 1; 2213 = 3^7 + 3^3  1; 2267 = 3^7 + 3^4  1; 2269 = 3^7 + 3^4 + 1; 2917 = 3^7 + 3^6 + 1, seven primes found, so a(7) = 7.


MATHEMATICA

Table[c1 = 3^i; cs = {};
Do[c2 = 3^j; cp = c1 + c2 + 1; If[PrimeQ[cp], cs = Union[cs, {cp}]];
cp = c1 + c2  1; If[PrimeQ[cp], cs = Union[cs, {cp}]];
cp = c1  c2 + 1; If[PrimeQ[cp], cs = Union[cs, {cp}]];
cp = c1  c2  1;
If[PrimeQ[cp], cs = Union[cs, {cp}]], {j, 1, i  1}];
Length[cs], {i, 2, 100}]
(* Alternative: *)
Table[s = 3^i; ct = 0; Do[t = 3^j; a1 = s + t; a2 = s  t; If[PrimeQ[a1 + 1], ct++]; If[PrimeQ[a1  1], ct++]; If[PrimeQ[a2 + 1], ct++]; If[PrimeQ[a2  1], ct++], {j, 1, i  1}]; ct, {i, 2, 100}] (* Lei Zhou, Mar 19 2015 *)


PROG

(PARI) a(n)=sum(k=0, n1, isprime(3^n3^k1)+isprime(3^n3^k+1)+isprime(3^n+3^k1)+isprime(3^n+3^k+1)) \\ Charles R Greathouse IV, Oct 06 2011


CROSSREFS

Cf. A196697.
Sequence in context: A319805 A055950 A294428 * A295079 A237047 A021806
Adjacent sequences: A196695 A196696 A196697 * A196699 A196700 A196701


KEYWORD

nonn


AUTHOR

Lei Zhou, Oct 05 2011


STATUS

approved



