A219280 - OEIS

%I #12 Oct 16 2013 11:16:21

%S 2,7,97,665857,708158977,150038171394905030432003281854339710977

%N Smallest prime of the form ChebyshevT[2^n, x].

%C ChebyshevT[2^n, x] is the 2^n th Chebyshev polynomial of the first kind evaluated at x.

%C The corresponding numbers x are {2, 2, 2, 3, 2, 8, 164, 29, ...}.

%C a(7) = T(128, 29) = 2518958009…2561281 contains 226 decimal digits.

%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 795.

%D C. W. Jones, J. C. P. Miller, J. F. C. Conn and R. C. Pankhurst, Tables of Chebyshev polynomials, Proc. Roy. Soc. Edinburgh. Sect. A. 62, (1946), 187-203.

%e T(1, x) = x => a(0) = T(1,2) = 2 ;

%e T(2, x) = 2x^2 - 1 => a(1) = T(2, 2) = 7 ;

%e T(4, x) = 8x^4 - 8x^2 + 1 => a(2) = T(4,2) = 97.

%t Table[k = 0; While[!PrimeQ[ChebyshevT[2^n,k]], k++]; ChebyshevT[2^n,k], {n, 0, 7}]

%Y Cf. A066436, A144131, A144132, A219276, A219277, A219278, A219279.

%K nonn

%O 0,1

%A _Michel Lagneau_, Nov 17 2012