login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A250844
Primes of the form 7^x + y^7 with x, y > 0.
2
16433, 33191, 134033, 6044737, 40633543, 50353607, 268435463, 268437857, 268452263, 274200257, 1977343127, 2245762199, 2494358231, 4471684631, 4586471767, 13841567137, 21870016807, 21870117649, 52523350487, 54500676887, 78364166497, 92205451297, 97157445863
OFFSET
1,1
COMMENTS
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
LINKS
EXAMPLE
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.
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
Cf. A250715.
Cf. similar sequences listed in A250481.
Sequence in context: A168633 A122714 A133533 * A076166 A168665 A283027
KEYWORD
nonn
AUTHOR
Vincenzo Librandi, Dec 01 2014
STATUS
approved