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A082101
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Primes of form 2^k + 3^k.
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32
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OFFSET
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1,1
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COMMENTS
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Next term, if it exists, is > 10^125074. - David Wasserman, Aug 13 2004
Since x+y is a factor of x^m+y^m if m is odd, 2^m+3^m is divisible by 2+3=5 unless m is zero or a power of 2. This is similar to Fermat numbers 1+2^m. - Michael Somos, Aug 27 2004
Checked k being powers of two through 2^21. Thus a(5) > 10^2000000. Primes of this magnitude are rare (about 1 in 4.6 million), so chance of finding one is remote with today's computer algorithms and speeds. - Robert Price, Apr 25 2013
If a(5) exists it is greater than 10^16000000. Probably finite and full. - Charles R Greathouse IV, Apr 29 2013
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LINKS
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Table of n, a(n) for n=1..4.
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EXAMPLE
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m=0: 1+1, m=1: 2+3, m=2: 4+9, m=4: 16+81.
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MATHEMATICA
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a={}; Do[If[PrimeQ[p=2^n+3^n], AppendTo[a, p]], {n, 0, 10^3}]; a (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)
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PROG
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(PARI) print1(2); for(n=0, 99, if(ispseudoprime(t=2^(2^n)+3^(2^n)), print1(", "t))) \\ Charles R Greathouse IV, Jul 19 2011
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CROSSREFS
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Cf. A094474-A094499.
Sequence in context: A075742 A075737 A100843 * A158712 A090472 A120266
Adjacent sequences: A082098 A082099 A082100 * A082102 A082103 A082104
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KEYWORD
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nonn,changed
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Apr 14 2003
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STATUS
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approved
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