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A219280
Smallest prime of the form ChebyshevT[2^n, x].
1
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.
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}]
KEYWORD
nonn
AUTHOR
Michel Lagneau, Nov 17 2012
STATUS
approved