A138920 -id:A138920 - cp's OEIS frontend

A138923 Indices k such that A020506(k)=Phi[k](-7) is prime, where Phi is a cyclotomic polynomial.

3, 9, 10, 15, 17, 23, 25, 26, 27, 28, 29, 36, 42, 47, 48, 61, 76, 84, 110, 126, 148, 210, 224, 262, 280, 288, 296, 298, 325, 327, 332, 352, 365, 456, 513, 528, 740, 1062, 1162, 1445, 1460, 1518, 1619, 1660, 2094, 2130, 2260, 2380, 3398, 3447, 3918

Offset: 1

M. F. Hasler, Apr 03 2008

nonn

There are only 6 terms between 365 and 1445 (exclusive).

Robert Price, Table of n, a(n) for n = 1..97
Yves Gallot, Cyclotomic polynomials and prime numbers

Cf. A020506, A138920-A138940.

Select[ Range[ 2400], PrimeQ[ Cyclotomic[#, -7]] &] (* Robert G. Wilson v, Mar 25 2012 *)

for( i=1,999, ispseudoprime( polcyclo(i,-7)) && print1( i",")) /* use ...subst(polcyclo(i),x,-7)... in PARI < 2.4.2 */

A138924 Indices k such that A020505(k)=Phi[k](-6) is prime, where Phi is a cyclotomic polynomial.

Original entry on oeis.org

3, 4, 6, 8, 9, 11, 14, 15, 21, 24, 25, 31, 42, 43, 45, 47, 58, 59, 77, 107, 124, 142, 144, 177, 192, 254, 279, 360, 407, 437, 480, 525, 542, 551, 579, 764, 811, 822, 891, 917, 1018, 1028, 1150, 1326, 1376, 1464, 1468, 1650, 1719, 1924, 2096, 2098, 2176, 2226

Offset: 1

M. F. Hasler, Apr 03 2008

nonn

Robert Price, Table of n, a(n) for n = 1..104
Yves Gallot, Cyclotomic polynomials and prime numbers

Cf. A020505, A138920-A138940.

Select[ Range[ 2000], PrimeQ[ Cyclotomic[#, -6]] &] (* Robert G. Wilson v, Mar 25 2012 *)

for( i=1,999, ispseudoprime( polcyclo(i,-6)) && print1( i",")) /* use ...subst(polcyclo(i),x,-6)... in PARI < 2.4.2 */

a(51)-a(54) from Robert Price, Apr 02 2012

A138925 Indices k such that A020504(k)=Phi[k](-5) is prime, where Phi is a cyclotomic polynomial.

Original entry on oeis.org

5, 6, 12, 14, 22, 24, 26, 28, 45, 48, 55, 56, 67, 88, 92, 94, 98, 99, 101, 103, 108, 114, 116, 120, 229, 236, 248, 254, 265, 282, 288, 298, 322, 347, 362, 384, 399, 420, 500, 536, 567, 615, 620, 714, 835, 992, 1047, 1064, 1238, 1794, 1858, 1962, 2313, 2397

Offset: 1

M. F. Hasler, Apr 03 2008

nonn

Robert Price, Table of n, a(n) for n = 1..114
Yves Gallot, Cyclotomic polynomials and prime numbers

Cf. A020504, A138920-A138940.

Select[ Range[ 2000], PrimeQ[ Cyclotomic[#, -5]] &] (* Robert G. Wilson v, Mar 25 2012 *)

for( i=1,999, ispseudoprime( polcyclo(i,-5)) && print1( i",")) /* use ...subst(polcyclo(i),x,-5)... in PARI < 2.4.2 */

a(53)-a(54) from Robert Price, Apr 05 2012

A138926 Indices k such that A020503(k)=Phi[k](-4) is prime, where Phi is a cyclotomic polynomial.

Original entry on oeis.org

3, 4, 8, 12, 16, 20, 28, 40, 60, 92, 96, 104, 140, 148, 156, 300, 356, 408, 596, 612, 692, 732, 756, 800, 952, 996, 1004, 1228, 1268, 2240, 2532, 3060, 3796, 3824, 3944, 5096, 5540, 7476, 7700, 8544, 9800, 14628, 15828, 16908, 18480, 20260, 21924, 24656, 38456

Offset: 1

M. F. Hasler, Apr 03 2008

nonn

It appears that for all k>1, a(k) is a multiple of 4.

It also appears that all Cyclotomic Polynomials, Phi[k](x), where k is a multiple of 4 have no odd powers of x. For example, Phi[20](x)=x^8-x^6+x^4-x^2+1. This implies that Phi[k](x)=Phi[k](-x), where k is a multiple of 4. - Robert Price, Apr 14 2012

Robert Price, Table of n, a(n) for n = 1..49
Yves Gallot, Cyclotomic polynomials and prime numbers

Cf. A020503, A138920-A138940.

Select[ Range[3, 5000], PrimeQ[ Cyclotomic[#, -4]] &] (* Robert G. Wilson v, Mar 25 2012 *)

for( i=1,999, ispseudoprime( polcyclo(i,-4)) && print1( i",")) /* use ...subst(polcyclo(i),x,-4)... in PARI < 2.4.2 */

a(36)-a(49) from Robert Price, Apr 07 2012

A138927 Indices k such that A020502(k)=Phi[k](-3) is prime, where Phi is a cyclotomic polynomial.

Original entry on oeis.org

3, 5, 6, 7, 12, 13, 14, 18, 23, 24, 26, 30, 35, 36, 40, 42, 43, 60, 65, 66, 72, 77, 108, 126, 132, 142, 206, 215, 236, 276, 281, 286, 290, 304, 322, 359, 364, 391, 464, 487, 510, 522, 528, 529, 535, 558, 574, 577, 672, 680, 713, 731, 760, 799, 828, 892, 984

Offset: 1

M. F. Hasler, Apr 03 2008

nonn

Robert Price, Table of n, a(n) for n = 1..157
Yves Gallot, Cyclotomic polynomials and prime numbers
Index entries for cyclotomic polynomials, values at X

Cf. A020502, A138920-A138940.

Select[ Range[3, 1000], PrimeQ[ Cyclotomic[#, -3]] &] (* Robert G. Wilson v, Mar 25 2012 *)

for( i=1,999, ispseudoprime( polcyclo(i,-3)) && print1( i","))

A138928 Indices n such that A020501(n) = phi(n)(-2) is prime, where Phi is a cyclotomic polynomial.

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 26, 30, 31, 32, 34, 38, 39, 40, 43, 45, 49, 54, 56, 61, 62, 63, 66, 75, 79, 80, 85, 87, 98, 101, 117, 120, 122, 127, 130, 138, 154, 161, 167, 170, 178, 183, 184, 186, 187, 191, 192, 199, 205, 207, 208

Offset: 1

M. F. Hasler, Apr 03 2008

nonn

While the sequence is not very interesting up to a(n)<300, there are only 4 values in the interval [400,599].

Robert Price, Table of n, a(n) for n = 1..227
Yves Gallot, Cyclotomic polynomials and prime numbers
Index entries for cyclotomic polynomials, values at X

Cf. A020501, A138920-A138940.

Select[ Range[3, 1000], PrimeQ[ Cyclotomic[#, -2]] &] (* Robert G. Wilson v, Mar 25 2012 *)

for( i=1,999, isprime( polcyclo(i,-2)) && print1( i",")) /* for PARI < 2.4.2 use ...subst(polcyclo(i),x,-2)...*/

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

Original entry on oeis.org

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

A291990 Primes of the form Phi(k, -10), where Phi is the cyclotomic polynomial.

Original entry on oeis.org

101, 9091, 909091, 9901, 909090909090909091, 99990001, 909090909090909090909090909091, 999999000001, 1111111111111111111, 11111111111111111111111, 9999999900000001, 9090909090909090909090909090909090909090909090909091

Offset: 1

Robert Price, Sep 07 2017

nonn

Robert Price, Table of n, a(n) for n = 1..18
Yves Gallot, Cyclotomic polynomials and prime numbers
Index entries for cyclotomic polynomials,values at X

Cf. A138920.

Select[Table[Cyclotomic[k,-10], {k, 3, 100}], PrimeQ[#] &]

cp's OEIS Frontend

A138923 Indices k such that A020506(k)=Phi[k](-7) is prime, where Phi is a cyclotomic polynomial.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

A138924 Indices k such that A020505(k)=Phi[k](-6) is prime, where Phi is a cyclotomic polynomial.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A138925 Indices k such that A020504(k)=Phi[k](-5) is prime, where Phi is a cyclotomic polynomial.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A138926 Indices k such that A020503(k)=Phi[k](-4) is prime, where Phi is a cyclotomic polynomial.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A138927 Indices k such that A020502(k)=Phi[k](-3) is prime, where Phi is a cyclotomic polynomial.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

A138928 Indices n such that A020501(n) = phi(n)(-2) is prime, where Phi is a cyclotomic polynomial.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI