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A072226 Numbers n such that the n-th cyclotomic polynomial evaluated at 2  (=A019320(n)) is prime. 18
2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 22, 24, 26, 27, 30, 31, 32, 33, 34, 38, 40, 42, 46, 49, 56, 61, 62, 65, 69, 77, 78, 80, 85, 86, 89, 90, 93, 98, 107, 120, 122, 126, 127, 129, 133, 145, 150, 158, 165, 170, 174, 184, 192, 195, 202, 208, 234, 254, 261 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The prime n in this sequence are in A000043, which produce the Mersenne primes. If 2p is in this sequence, with p prime, then p is a Wagstaff number, A000978. - T. D. Noe, Apr 02 2008

While the sequence looks quite dense for small values, note that there are only 10 values in the interval [700,1200]. - M. F. Hasler, Apr 03 2008

REFERENCES

Yves Gallot, Cyclotomic polynomials and prime numbers (November 12, 2000; revised January 5, 2001)

LINKS

T. D. Noe, Table of n, a(n) for n=1..277 (initial 234 terms from Yves Gallot)

Joerg Arndt, Matters Computational (The Fxtbook)

Yves Gallot, Cyclotomic polynomials and prime numbers

Index entries for cyclotomic polynomials, values at X

MATHEMATICA

Select[Range[600], PrimeQ[Cyclotomic[ #, 2]]&]

PROG

(PARI) for( i=1, 999, ispseudoprime( polcyclo(i, 2)) &&& print1( i", ")) /* for PARI < 2.4.2 use ...subst(polcyclo(i), x, 2)... */ \\ M. F. Hasler, Apr 03 2008

CROSSREFS

Corresponding primes are listed in A292015.

Cf. A138920-A138940.

Sequence in context: A328869 A004744 A171987 * A247809 A247802 A245028

Adjacent sequences:  A072223 A072224 A072225 * A072227 A072228 A072229

KEYWORD

nonn

AUTHOR

Reiner Martin (reinermartin(AT)hotmail.com), Jul 04 2002

EXTENSIONS

Edited by Max Alekseyev, Apr 25 2018

STATUS

approved

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Last modified March 30 16:16 EDT 2020. Contains 333127 sequences. (Running on oeis4.)