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Search: id:A094493
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| A094493 |
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Primes p such that 2^j+p^j are primes for j=0,1,2,16. |
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| 43577, 84317, 93887, 108377, 124247, 346667, 379997, 431867, 461297, 579197, 681257, 819317, 863867, 889037, 1143047, 1146797, 1271027, 1306817, 1518707, 1775867, 1926647, 1948517, 2119937, 2177447, 2348807, 2491607, 2604557
(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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For j=0: 1+1=2 is prime; other conditions are:
because of p^1+2=prime; 3rd and 4th conditions are as
follows: prime=p^2+4 and prime=65536+p^16.
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MATHEMATICA
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{ta=Table[0, {100}], u=1}; Do[s0=2; s1=2+Prime[j]^1; s2=4+Prime[j]^2; s16=65536+Prime[j]^16 If[PrimeQ[s0]&&PrimeQ[s1]&&PrimeQ[s2]&&PrimeQ[s16], 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-A094491.
Sequence in context: A146074 A126771 A103875 this_sequence A165479 A140931 A045157
Adjacent sequences: A094490 A094491 A094492 this_sequence A094494 A094495 A094496
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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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