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Search: id:A094494
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| A094494 |
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Primes p such that 2^j+p^j are primes for j=0,2,4,8. |
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3
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| 6203, 16067, 72367, 105653, 179743, 323903, 1005467, 1040113, 1276243, 1331527, 1582447, 1838297, 1894873, 2202433, 2314603, 2366993, 2369033, 2416943, 2533627, 2698697, 2804437, 2806613, 2823277, 2826337, 2851867, 2888693
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes of 2^j+p^j form are a generalization of Fermat-primes. 1^j is replaced by p^j. This is strongly supported by the observation that corresponding j-exponents are apparently powers of 2 like for the 5 known Fermat primes. See A094473-A094491.
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EXAMPLE
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Conditions mean 2,p^2+4,16+p^4,256+p^8 are all primes.
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MATHEMATICA
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{ta=Table[0, {100}], u=1}; Do[s0=2; s2=4+Prime[j]^2; s2=16+Prime[j]^4; s8=256+Prime[j]^8 If[PrimeQ[s0]&&PrimeQ[s2]&&PrimeQ[s4]&&PrimeQ[s8], Print[{j, Prime[j]}]; ta[[u]]=Prime[j]; u=u+1], {j, 1, 1000000}]
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CROSSREFS
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Cf. A082101, A094473-A094492.
Sequence in context: A114930 A068757 A031836 this_sequence A112665 A092726 A028545
Adjacent sequences: A094491 A094492 A094493 this_sequence A094495 A094496 A094497
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 01 2004
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