

A196778


a(n) is the number of primes in the form of 4^n+/4^k+/1, while 0 <= k < n.


1



1, 3, 5, 6, 7, 7, 9, 8, 9, 12, 7, 9, 4, 4, 8, 11, 6, 11, 7, 8, 14, 7, 8, 11, 6, 10, 9, 8, 8, 11, 6, 10, 13, 7, 6, 9, 10, 8, 8, 10, 5, 10, 15, 6, 11, 9, 14, 7, 8, 16, 12, 10, 5, 10, 9, 8, 10, 8, 7, 10, 11, 13, 12, 6, 12, 9, 4, 10, 12, 13, 8, 14, 7, 2, 13, 7
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OFFSET

1,2


COMMENTS

Conjecture: all elements of this sequence is greater than 0.
Conjecture tested hold up to n=2355. Further test is still running
The Mathematica program gives the first 100 terms.
Terms for all n are tend to be small integers.
4^n+/4^k+/1=2^2n+/2^2k+/1


LINKS



EXAMPLE

n=1, 2=4^14^04^0, 1 prime found, so a(1)=1;
n=2, 11=4^24^11; 13=4^24^1+1; 19=4^2+4^11, 3 primes found, so a(2)=3;
...
n=13, 67043329=4^134^8+1; 67104769=4^134^6+1; 67108859=4^134^11; 67108879=4^13+4^21, 4 primes found, so a(13)=4;


MATHEMATICA

b = 4; Table[c1 = b^i; cs = {};
Do[c2 = b^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, 0, i  1}];
ct = Length[cs]; ct, {i, 1, 100}]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



