| Displaying 1-3 of 3 results found. page 1 Primes of the form 3*m^2 - 8. +10
5 19, 67, 139, 499, 859, 1579, 1867, 2179, 3259, 4099, 6067, 6619, 8419, 9067, 9739, 22699, 25939, 27067, 28219, 38299, 39667, 46867, 54667, 56299, 61339, 63067, 73939, 79699, 81667, 89779, 91867, 93979, 100459, 102667, 114067, 123619 MATHEMATICA Select[Table[3n^2 - 8, {n, 2, 1000}], PrimeQ] PROG (Magma) [a: n in [2..300] | IsPrime(a) where a is 3*n^2-8]; Dimension of the space of weight 2n cuspidal newforms for Gamma_0(45). +10
2 1, 5, 9, 11, 15, 19, 21, 25, 29, 31, 35, 39, 41, 45, 49, 51, 55, 59, 61, 65, 69, 71, 75, 79, 81, 85, 89, 91, 95, 99, 101, 105, 109, 111, 115, 119, 121, 125, 129, 131, 135, 139, 141, 145, 149, 151, 155, 159, 161, 165 COMMENTS The sequence lists the odd numbers ending with 1, 5 and 9. This follows from Mathar's generating function. - Bruno Berselli, Feb 16 2016 FORMULA G.f.: x - x^2*(-5-4*x-2*x^2+x^3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Jul 15 2015 a(n) = 4*n - 2*floor(n/3 - 1/3) - 3. This formula follows from Mathar's generating function. - Bruno Berselli, Feb 16 2016 1, -2, 4, -4, 6, -8, 10, -9, 11, -14, 16, -14, 16, -20, 22, -19, 21, -26, 28, -24, 26, -32, 34, -29, 31, -38, 40, -34, 36, -44, 46, -39, 41, -50, 52, -44, 46, -56, 58, -49, 51, -62, 64, -54, 56, -68, 70, -59, 61, -74, 76, -64, 66, -80, 82, -69, 71, -86, 88, -74, 76, -92, 94, -79, 81, -98, 100, -84 COMMENTS a(-1)=1=a(0). a(n) - a(n-1) = b(n) = 0, -3, 6, -8, 10, -14, 18, -19, 20, -25, 30, -30, 30, -36, 42, -41, ... . Missing terms in abs(a(n)): PIII(n) = 0, 3, 5, 7, 12, 13, 15, 17, 18, 23, 25, 27, 30, 33, 35, 37, 42, ... . See A063241(n+1) and 6* A047222(n+1). FORMULA a(4*n) = 1+5*n, a(1+4*n) = -2-6*n, a(2+4*n) = 4+6*n, a(3+4*n) = -4-5*n. a(n+4) - a(n) = period of length 4: repeat 5,-6, 6, -5. a(n) = 2*a(n-4) + a(n-8). G.f. ( -1+x-3*x^2-3*x^4+x^3+x^5-x^6 ) / ( (x-1)*(1+x)^2*(x^2+1)^2 ). - R. J. Mathar, Aug 07 2012 a(n) = (5+(2*n+1)*(11*(-1)^n-(-1)^((2*n-1+(-1)^n)/4))+(-1)^((6*n-1 +(-1)^n)/4))/16. - Luce ETIENNE, Jun 05 2015 MATHEMATICA a[n_] := Switch[Mod[n, 4], 0, 5n/4+1, 1, (-3n-1)/2, 2, 3n/2+1, 3, (-5n-1)/4]; Table[a[n], {n, 0, 67}] (* Jean-François Alcover, Nov 08 2012 *) Search completed in 0.002 seconds | 