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A098717
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Primes p such that 2*p+1 and ((2*p+1)^2+1)/2=p^2+(p+1)^2 are primes.
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1
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2, 5, 29, 719, 1229, 1409, 1559, 2039, 2399, 2699, 2939, 3449, 3779, 6269, 6899, 7079, 8069, 9689, 12959, 13619, 14009, 14249, 14879, 19559, 20369, 20759, 21089, 22079, 22469, 23459, 26879, 28559, 30269, 31799, 32009, 32789, 33179, 33569, 38639, 39989, 40949, 41399, 41969, 42359, 45569, 46349, 47279, 49499, 49919, 53309, 54959, 55469
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| It is easy to prove that all the terms except the first two must be =9(mod 10).
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EXAMPLE
| a(3)=29=p and 2*p+1=59 and (59^2+1)/2=29^2+30^2=1741 are prime
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MATHEMATICA
| Flatten[Append[{2, 5}, Select[Sort[Range[29, 30000000, 30], Range[49, 30000000, 30]], PrimeQ[ # ]&&PrimeQ[2 # + 1] && PrimeQ[1 + 2 # + 2 #^2] &]]] (Zak Seidov)
f1[n_]:=(n+1)^2-n^2; f2[n_]:=(n+1)^2+n^2; Select[Prime[Range[8! ]], PrimeQ[f1[ # ]]&&PrimeQ[f2[ # ]]&] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 25 2010]
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CROSSREFS
| Cf. A082612.
Sequence in context: A179823 A064098 A181078 * A059784 A000283 A121910
Adjacent sequences: A098714 A098715 A098716 * A098718 A098719 A098720
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KEYWORD
| nonn
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AUTHOR
| Robin Garcia (verob99(AT)teleline.es), Sep 29 2004
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EXTENSIONS
| More terms from Zak Seidov (zakseidov(AT)yahoo.com), Feb 16 2005
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