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A098717 Primes p such that 2*p+1 and ((2*p+1)^2 + 1)/2 = p^2 + (p+1)^2 are primes. 1
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; text; internal format)
OFFSET

1,1

COMMENTS

It is easy to prove that all the terms except the first two must satisfy a(n) mod 10 = 9.

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

a(3) = 29 = p and 2*p + 1 = 59 and (59^2 + 1)/2 = 29^2 + 30^2 = 1741 are prime.

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[ # ]]&] (* Vladimir Joseph Stephan Orlovsky, Feb 25 2010 *)

CROSSREFS

Cf. A082612.

Sequence in context: A064098 A181078 A265773 * A059784 A000283 A121910

Adjacent sequences:  A098714 A098715 A098716 * A098718 A098719 A098720

KEYWORD

nonn

AUTHOR

Robin Garcia, Sep 29 2004

EXTENSIONS

More terms from Zak Seidov, Feb 16 2005

STATUS

approved

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Last modified August 6 19:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)