

A196697


Number of primes in the form of 2^n +/ 2^k +/ 1 with 0 <= k < n.


7



1, 4, 5, 6, 7, 9, 7, 11, 10, 12, 7, 12, 8, 12, 9, 14, 11, 19, 13, 22, 7, 9, 11, 16, 4, 8, 9, 7, 12, 18, 14, 15, 11, 10, 10, 18, 8, 12, 11, 18, 12, 23, 5, 12, 13, 16, 13, 22, 8, 9, 16, 13, 9, 13, 14, 11, 11, 10, 10, 20, 15, 10, 10, 13, 9, 22, 11, 10, 10, 12
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Conjecture: all elements of this sequence are greater than 0.
Conjecture tested holds up to n=10000, as of in bfile.
Terms for all n are tend to be small integers.
All Mersenne primes, 3*2^n+/1, 5*2^n+/1, 7*2^n+/1, 15*2^n+/1 primes are sub group of this type of primes.
A prime that is explicitly found for this type is 2^10485762^8912321.
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


LINKS

Lei Zhou, Table of n, a(n) for n = 1..10000
Chris Caldwell, ed., 2^10485762^8912321


EXAMPLE

n=1, 2=2^1+2^01=2^12^0+1 is prime, so a(1)=1;
n=2, 2=2^22^01; 3=2^22^1+1; 5=2^2+2^11=2^22^1+1; 7=2^2+2^1+1, four primes found, so a(2)=4;
...
n=11,2017=2^112^5+1;2039=2^112^31;2053=2^11+2^2+1;2063=2^11+2^41;2081=2^11+2^5+1;2111=2^11+2^61;2113=2^11+2^6+1, 7 primes found, so a(11)=7


MATHEMATICA

Table[c1 = 2^i; cs = {};
Do[c2 = 2^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}];
Length[cs], {i, 1, 100}]


PROG

(PARI) a(n)=my(v=List(), t); for(k=0, n1, if(isprime(t=2^n2^k1), listput(v, t)); if(isprime(t=2^n2^k+1), listput(v, t)); if(isprime(t=2^n+2^k1), listput(v, t); if(isprime(t=2^n+2^k+1), listput(v, t)))); #Set(v) \\ Charles R Greathouse IV, Oct 06 2011


CROSSREFS

Cf. A238900 (least k).
Sequence in context: A075341 A143789 A068521 * A068318 A242337 A201739
Adjacent sequences: A196694 A196695 A196696 * A196698 A196699 A196700


KEYWORD

nonn


AUTHOR

Lei Zhou, Oct 05 2011


STATUS

approved



