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A066049
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Numbers n such that 2*n^2 - 1 is a prime.
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18
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2, 3, 4, 6, 7, 8, 10, 11, 13, 15, 17, 18, 21, 22, 24, 25, 28, 34, 36, 38, 39, 41, 42, 43, 45, 46, 49, 50, 52, 56, 59, 62, 63, 64, 69, 73, 76, 80, 81, 85, 87, 91, 92, 95, 98, 102, 108, 109, 112, 113, 115, 118, 125, 126, 127, 132, 134, 137, 140, 141, 143, 153, 154, 155
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| It is conjectured that this sequence is infinite.
A066436 gives resulting primes p such that (p+1)/2 is square. - Chandler
a(n) = A160697(n+1). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 24 2009]
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REFERENCES
| D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 31.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| a(n) = A090697(n)/2 = A110558(n)/4. - Chandler
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MATHEMATICA
| Select[Range[200], PrimeQ[2#^2-1]&] (* From Harvey P. Dale, June 14 2011 *)
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PROG
| (PARI) { n=0; for (m=1, 10^9, if (isprime(2*m^2 - 1), write("b066049.txt", n++, " ", m); if (n==1000, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 08 2009]
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CROSSREFS
| Cf. A028870, A066436, A090697, A091176, A110558.
Sequence in context: A027564 A186511 * A160697 A131629 A167701 A114149
Adjacent sequences: A066046 A066047 A066048 * A066050 A066051 A066052
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 09 2002
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EXTENSIONS
| Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 15 2005
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