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A089485
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Numbers k such that k^4 + 4^k = A001589(k) is a semiprime.
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0
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OFFSET
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1,1
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COMMENTS
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For n = 2*k + 1, n^4 + 4^n = (n^2 + n*2^(k + 1) + 2^n) * (n^2 - n*2^(k + 1) + 2^n) The sequence gives those values of n for which both parentheses are primes. No further terms were found for k<=5000.
a(6) > 120000, if it exists. - Tyler Busby, Feb 13 2023
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LINKS
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EXAMPLE
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a(1)=3 because 3^4+4^3=145=5*29, a(2)=5 because 5^4+4^5=1649=17*97.
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MATHEMATICA
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Select[Range[60], PrimeOmega[#^4+4^#]==2&] (* Harvey P. Dale, Jul 31 2020 *)
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PROG
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(PARI) for(k=0, 5000, my(n=2*k+1, p1=n^2+n*2^(k+1)+2^n, p2=n^2-n*2^(k+1)+2^n); if(ispseudoprime(p1)&&ispseudoprime(p2), print1(n, ", "))) \\ Hugo Pfoertner, Jul 24 2019
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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