A219280 Smallest prime of the form ChebyshevT[2^n, x].

2, 7, 97, 665857, 708158977, 150038171394905030432003281854339710977

Offset

0,1

Comments

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

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

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

References

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.

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.

Links

Table of n, a(n) for n=0..5.

Example

T(1, x) = x => a(0) = T(1,2) = 2 ;
T(2, x) = 2x^2 - 1 => a(1) = T(2, 2) = 7 ;
T(4, x) = 8x^4 - 8x^2 + 1 => a(2) = T(4,2) = 97.

Mathematica

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

Crossrefs

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

Sequence in context: A102344 A087589 A002812 * A277434 A322642 A192342

Adjacent sequences: A219277 A219278 A219279 * A219281 A219282 A219283

Keyword

nonn

Author

Michel Lagneau, Nov 17 2012

Status

approved