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A098828
Primes of the form 2*n^2 + 2*n - 1.
7
3, 11, 23, 59, 83, 179, 263, 311, 419, 479, 683, 839, 1103, 1511, 2111, 2243, 2663, 2963, 3119, 4139, 4703, 5099, 5303, 5939, 7079, 10223, 11399, 12011, 12323, 12959, 17483, 19403, 21011, 21839, 22259, 24419, 25763, 27143, 27611, 28559, 30011
OFFSET
1,1
COMMENTS
a(n)==3 (mod 4).
Equivalently primes p such that 2p+3 is square.
Also 3 followed by primes p of the form 2*n^2+6*n+3 = 2*(n+2)^2-2*(n+2)-1 (see the first comment) such that 2^(p-1)+3 is not prime. - Vincenzo Librandi, Jan 03 2009; M. F. Hasler, Jan 07 2009; R. J. Mathar, Jan 14 2009; Bruno Berselli, Sep 23 2013
LINKS
FORMULA
a(n) = (A109367(n) - 3)/2.
MATHEMATICA
Select[Table[Prime[n], {n, 3500}], IntegerQ[(2# + 3)^(1/2)] &] (* Ray Chandler, Oct 26 2004 *)
PROG
(Magma) [3] cat [ p: p in PrimesUpTo(30100) | exists(t){ n: n in [1..Isqrt(p div 2)] | 2*n^2+6*n+3 eq p } and not IsPrime(2^(p-1)+3) ];
(PARI) list(lim)=my(v=List()); for(n=1, oo, my(t=2*n*(n+1)-1); if(t>lim, return(Vec(v))); if(isprime(t), listput(v, t))) \\ Charles R Greathouse IV, Feb 26 2025
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Giovanni Teofilatto, Oct 09 2004
EXTENSIONS
Corrected by Ray Chandler, Oct 26 2004
Edited by N. J. A. Sloane, Jan 25 2009
Name edited by Charles R Greathouse IV, Feb 26 2025
STATUS
approved