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Search: id:A158361
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| A158361 |
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Primes p with property that p^4+2^4 is prime |
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+0
2
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| 3, 5, 7, 11, 13, 17, 19, 23, 37, 41, 59, 61, 71, 79, 97, 131, 139, 179, 223, 227, 229, 241, 283, 313, 317, 359, 367, 379, 383, 389, 439, 449, 461, 487, 503, 521, 569, 593, 617, 619, 631, 661
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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1) Q=(p^2)^2+4^2 only for Q=4k+1 (because of Fermat/Euler/Lagrange theorem)
2) Q has divisor 17 if p=17k +/- 4 or p=17k +/- 16
3) Sequence starts with first 10 odd primes
4) It is conjectured that sequence a(n) is infinite
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REFERENCES
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Leonard E. Dickson, History of the Theory of Numbers
Richard Guy, Unsolved Problems in Number Theory
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FORMULA
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p and Q=p^4+2^4 both prime
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EXAMPLE
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p=3: 3^4+2^4=97 prime => a(1)=3
p=29: 29^4+2^4=707297 = 73 x 9689 no prime, so 29 no member
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CROSSREFS
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Cf. A062324 A157950 A157764.
Sequence in context: A120334 A000978 A128925 this_sequence A131261 A100276 A065389
Adjacent sequences: A158358 A158359 A158360 this_sequence A158362 A158363 A158364
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KEYWORD
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nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 17 2009
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