A138940 -id:A138940 - cp's OEIS frontend

A138938 Indices k such that A019326(k)=Phi[k](8) is prime, where Phi is a cyclotomic polynomial.

1, 3, 9, 30, 42, 78, 87, 138, 189, 303, 318, 330, 408, 462, 504, 561, 1002, 1389, 1746, 1794, 2040, 2418, 2790, 3894, 4077, 4722, 6738, 10641, 14610, 14616, 15294, 16662, 18966, 19059, 26142, 27144, 28299, 31638, 33639, 39360

Offset: 1

M. F. Hasler, Apr 03 2008

nonn

Cf. A019326, A138920-A138940.

Select[Range[1000], PrimeQ[Cyclotomic[#, 8]] &]

for( i=1,999, ispseudoprime( polcyclo(i,8)) && print1( i",")) /* use ...subst( polcyclo(i),x,8)... in PARI < 2.4.2 */

a(17)-a(40) from Robert Price, Apr 20 2012

A138922 Indices k such that A020507(k)=Phi[k](-8) is prime, where Phi is a cyclotomic polynomial.

Original entry on oeis.org

6, 15, 18, 21, 39, 69, 159, 165, 174, 231, 378, 408, 501, 504, 606, 873, 897, 1122, 1209, 1395, 1947, 2040, 2361, 2778, 3369, 7305, 7647, 8154, 8331, 9483, 13071, 14616, 15819, 20301, 21282, 27144, 31083, 34725, 35775, 36855, 38118, 39360

Offset: 1

M. F. Hasler, Apr 03 2008

Yves Gallot, Cyclotomic polynomials and prime numbers

Cf. A020507, A138920-A138940.

Select[Range[1000], PrimeQ[Cyclotomic[#, -8]] &]

for( i=1,999, ispseudoprime( polcyclo(i,-8)) && print1( i",")) /* use ...subst(polcyclo(i),x,-8)... in PARI < 2.4.2 */

a(18)-a(42) from Robert Price, Mar 25 2012

A292014 Primes of the form Phi(k, 10), where Phi is the cyclotomic polynomial.

Original entry on oeis.org

11, 101, 9091, 9901, 909091, 1111111111111111111, 11111111111111111111111, 99990001, 999999000001, 909090909090909091, 900900900900990990990991, 9999999900000001, 909090909090909090909090909091, 900900900900900900900900900900990990990990990990990990990991

Offset: 1

Robert Price, Sep 07 2017

nonn

Robert Price, Table of n, a(n) for n = 1..19
Yves Gallot, Cyclotomic polynomials and prime numbers
Index entries for cyclotomic polynomials,values at X

Cf. A138940.

Select[Table[Cyclotomic[k,10], {k, 0, 100}], PrimeQ[#] &]

A252353 Numbers k such that Phi(k, 12) is prime, where Phi is the cyclotomic polynomial.

Original entry on oeis.org

1, 2, 3, 5, 10, 12, 19, 21, 22, 56, 60, 63, 70, 80, 84, 92, 97, 109, 111, 123, 164, 189, 218, 276, 317, 353, 364, 386, 405, 456, 511, 636, 675, 701, 793, 945, 1090, 1268, 1272, 1971, 2088, 2368, 2482, 2893, 2966, 3290, 4161, 4320, 4533, 4744, 6357, 7023, 7430, 7737, 9499, 9739

Offset: 1

Eric Chen, Dec 16 2014

nonn

Numbers k such that A019330(k) is prime.
With some exceptions, terms of sequence are such that 12^n - 1 has only one primitive prime factor. 20 is an instance of such an exception, since 12^20 - 1 has a single primitive prime factor, 85403261, but Phi(20, 12) is divisible by 5, it is not prime.
a(n) is a duodecimal unique period length.

			n         Phi(n, 12)
1         11
2         13
3         157
4         5 * 29
5         22621
6         7 * 19
7         659 * 4943
8         89 * 233
9         37 * 80749
10        19141
11        11 * 23 * 266981089
12        20593
etc.

Cf. A019330, A072226, A138919-A138940.

Select[Range[1728], PrimeQ[Cyclotomic[#, 12]] &]

for( i=1, 1728, ispseudoprime( polcyclo(i, 12)) && print1( i", "))

More terms from Michel Marcus, Dec 18 2014

More terms from Amiram Eldar, Mar 26 2021

cp's OEIS Frontend

A138938 Indices k such that A019326(k)=Phi[k](8) is prime, where Phi is a cyclotomic polynomial.

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A138922 Indices k such that A020507(k)=Phi[k](-8) is prime, where Phi is a cyclotomic polynomial.

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A292014 Primes of the form Phi(k, 10), where Phi is the cyclotomic polynomial.

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A252353 Numbers k such that Phi(k, 12) is prime, where Phi is the cyclotomic polynomial.

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