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A081091 Primes of the form 2^i + 2^j + 1, i>j>0. 15
7, 11, 13, 19, 37, 41, 67, 73, 97, 131, 137, 193, 521, 577, 641, 769, 1033, 1153, 2053, 2081, 2113, 4099, 4129, 8209, 12289, 16417, 18433, 32771, 32801, 32833, 40961, 65539, 133121, 147457, 163841, 262147, 262153, 262657, 270337, 524353, 524801 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A000120(a(n))=3.

This is sequence A070739 without the Fermat primes, A000215. Sequence A081504 lists the i for which there are no primes. - T. D. Noe, Jun 22 2007

Primes in A014311. - Reinhard Zumkeller, May 03 2012

LINKS

T. D. Noe and Robert Israel, Table of n, a(n) for n = 1..7800 (n = 1..1000 from T. D. Noe)

Richard Ehrenborg and N. Bradley Fox, The Descent Set Polynomial Revisited, arXiv:1408.6858, 2014

Norman B. Fox, Combinatorial Potpourri: Permutations, Products, Posets, and Pfaffians, University of Kentucky, Theses and Dissertations, Mathematics, Paper 25.

EXAMPLE

7 = 2^2 + 2^1 + 1

11 = 2^3 + 2^1 + 1

13 = 2^3 + 2^2 + 1

19 = 2^4 + 2^1 + 1

37 = 2^5 + 2^2 + 1

41 = 2^5 + 2^3 + 1

67 = 2^6 + 2^1 + 1

73 = 2^6 + 2^3 + 1

97 = 2^6 + 2^5 + 1

131 = 2^7 + 2^1 + 1

137 = 2^7 + 2^3 + 1

193 = 2^7 + 2^6 + 1

521 = 2^9 + 2^3 + 1

MAPLE

N:= 20: # to get all terms < 2^N

select(isprime, [seq(seq(2^i+2^j+1, j=1..i-1), i=1..N-1)]); # Robert Israel, May 17 2016

MATHEMATICA

Select[Flatten[Table[2^i + 2^j + 1, {i, 21}, {j, i-1}]], PrimeQ] (* Alonso del Arte, Jan 11 2011 *)

PROG

(PARI) N=41; B(x)={nB=floor(log(x)/log(2)); z=0;

for(i=0, nB, if(bittest(x, i), z++; if(z>3, return(0); ); ); );

if(z == 3, return(1); , return(0); ); };

x=6; while(N, x=nextprime(x); if(B(x), print1(x, ", "); N--; ); x++; ); \\ Washington Bomfim, Jan 11 2011

(PARI) do(mx)=my(v=List(), t); for(i=2, mx, for(j=1, i-1, if(ispseudoprime(t=2^i+2^j+1), listput(v, t)))); Vec(v) \\ Charles R Greathouse IV, Jan 02 2014

(PARI) is(n)=hammingweight(n)==3 && isprime(n) \\ Charles R Greathouse IV, Aug 28 2017

(Haskell)

a081091 n = a081091_list !! (n-1)

a081091_list = filter ((== 1) . a010051') a014311_list

-- Reinhard Zumkeller, May 03 2012

CROSSREFS

Essentially the same as A070739.

Cf. A000040, A000215, A081092, A010051.

Cf. A095077 (primes with four bits set).

Sequence in context: A059308 A075521 A084444 * A027901 A129213 A110966

Adjacent sequences:  A081088 A081089 A081090 * A081092 A081093 A081094

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Mar 05 2003

STATUS

approved

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Last modified July 23 21:46 EDT 2021. Contains 346265 sequences. (Running on oeis4.)