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Search: id:A094491
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| A094491 |
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Primes p such that 2^j+p^j are primes for j=0,4,8,128. |
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+0
4
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| 223, 2104547, 2403689, 4268233, 17620457, 21848647, 23487311, 29205821, 42889591, 43458859, 47899487, 48309017, 54666847, 61227457, 73038689, 81742547, 83574457, 85031153, 87285403, 95017003, 100339517, 103136867
(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. 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-A094490.
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EXAMPLE
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For j=0 1+1=2 is prime; other conditions are: because of p^4+16==prime; 3rd and 4th conditions are as follows: prime=p^8+256 and prime=2^128+p^128.
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MATHEMATICA
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{ta=Table[0, {100}], u=1}; Do[s0=2; s4=16+Prime[j]^4; s8=256+Prime[j]^8; s128=2^128+Prime[j]^128 If[PrimeQ[s0]&&PrimeQ[s4]&&PrimeQ[s8]&&PrimeQ[s128], 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-A094490.
Sequence in context: A152834 A139233 A153165 this_sequence A162604 A050241 A046296
Adjacent sequences: A094488 A094489 A094490 this_sequence A094492 A094493 A094494
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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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EXTENSIONS
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a(5)-a(22) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Oct 12 2008
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