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Search: id:A100266
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| A100266 |
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Primes of the form x^16 + y^16. |
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2
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| 2, 65537, 4338014017, 2973697798081, 36054040477057, 314707907280257, 184884411482927041, 665698084159890497, 675416609183179841, 2177953490397261761, 8746361693522261761, 18492693803573123777
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The Mathematica program generates numbers of the form x^16 + y^16 in order of increasing magnitude; it accepts a number when it is prime.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Generalized Fermat Number
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MATHEMATICA
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n=4; pwr=2^n; xmax=2; r=Range[xmax]; num=r^pwr+r^pwr; Table[While[p=Min[num]; x=Position[num, p][[1, 1]]; y=r[[x]]; r[[x]]++; num[[x]]=x^pwr+r[[x]]^pwr; If[x==xmax, xmax++; AppendTo[r, xmax+1]; AppendTo[num, xmax^pwr+(xmax+1)^pwr]]; !PrimeQ[p]]; p, {15}]
q=16; lst={}; Do[Do[p=n^q+m^q; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 5!}], {m, 0, 5!}]; lst; Length[lst]; Take[Union[lst], 55] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 21 2009]
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CROSSREFS
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Cf. A100267 (primes of the form x^32 + y^32), A006686 (primes of the form x^8 + y^8), A002645 (primes of the form x^4 + y^4), A002313 (primes of the form x^2 + y^2).
Sequence in context: A052427 A051833 A060895 this_sequence A071067 A060069 A114950
Adjacent sequences: A100263 A100264 A100265 this_sequence A100267 A100268 A100269
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Nov 11 2004
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