A050268 - OEIS

%I #35 Dec 04 2024 10:34:43

%S 2753,1979,1277,647,89,359,953,1619,2357,3167,4049,5003,6029,7127,

%T 8297,9539,10853,12239,13697,15227,16829,18503,20249,22067,23957,

%U 25919,27953,30059,32237,34487,36809,41669,44207,46817,49499,52253

%N Primes of the form 36*k^2 - 810*k + 2753, listed in order of increasing parameter k >= 0.

%C The sequence of primes of this form, in order of increasing size, would read: 89, 359, 647, 953, 1277, 1619, 1979, 2357, 2753, ... - _M. F. Hasler_, Jan 18 2015

%C The polynomial is a transformed version of the polynomial P(x) = 36*x^2 + 18*x - 1801 whose absolute value gives 45 distinct primes for -33 <= x <= 11, found by Ruby in 1989. In the present sequence only positive values of the polynomial are taken into account. A117081 provides also the negative function values. - _Hugo Pfoertner_, Dec 13 2019

%D Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag New York, 2004.

%H Vincenzo Librandi, <a href="/A050268/b050268.txt">Table of n, a(n) for n = 1..10000</a>

%H Jitender Singh, <a href="https://arxiv.org/abs/2411.18366">Prime numbers and factorization of polynomials</a>, arXiv:2411.18366 [math.NT], 2024.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>.

%p t1:=[seq(36*n^2 - 810*n + 2753,n=0..100)]; t2:=[]; for i from 1 to nops(t1) do if isprime(t1[i]) then t2:=[op(t2),t1[i]]; fi; od: t2; # _N. J. A. Sloane_

%t Select[Table[36n^2-810n+2753,{n,0,2000}],PrimeQ] (* _Vincenzo Librandi_, Dec 08 2011 *)

%o (PARI) select(isprime, vector(1000, n, 36*n^2-810*n+2753)) \\ _Charles R Greathouse IV_, Feb 14 2011

%o (Magma) [a: n in [0..100] | IsPrime(a) where a is  36*n^2 - 810*n + 2753]; // _Vincenzo Librandi_, Dec 08 2011

%Y Cf. A022464, A117081.

%K nonn,easy,less

%O 1,1

%A _Eric W. Weisstein_

%E Definition corrected by _M. F. Hasler_, Jan 18 2015