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A250844
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Primes of the form 7^x + y^7 with x, y > 0.
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2
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16433, 33191, 134033, 6044737, 40633543, 50353607, 268435463, 268437857, 268452263, 274200257, 1977343127, 2245762199, 2494358231, 4471684631, 4586471767, 13841567137, 21870016807, 21870117649, 52523350487, 54500676887, 78364166497, 92205451297, 97157445863
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OFFSET
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1,1
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COMMENTS
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Conjecture: a(n+1)>=a(n)+42, with equality for infinitely many n,
namely those of the form a(n)=7^1+y^7, a(n+1)=7^2+y^7. - Robert Israel, May 09 2018
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LINKS
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EXAMPLE
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16433 is in this sequence because 16433 is prime and 7^2+3^7 = 16433.
33191 is in this sequence because 33191 is prime and 7^5+4^7 = 33191.
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MAPLE
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N:= 10^12: # to get all terms <= N
sort(select(isprime, [seq(seq(7^x+y^7, y=2..floor((N-7^x)^(1/7)), 2), x=1..floor(log[7](N)))])); # Robert Israel, May 09 2018
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MATHEMATICA
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f[x_, y_]:= 7^x + y^7; lst={}; Do[p=f[x, y]; If[PrimeQ[p], AppendTo[lst, p]], {y, 50}, {x, 50}]; Take[Union[lst], 30]
With[{nn=40}, Take[Sort[Select[7^#[[1]]+#[[2]]^7&/@Tuples[Range[nn], 2], PrimeQ]], nn]] (* Harvey P. Dale, May 28 2015 *)
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CROSSREFS
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Cf. similar sequences listed in A250481.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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