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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.)