A020504 -id:A020504 - cp's OEIS frontend

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

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

A179897 a(n) = (n^(2*n+1) + 1) / (n+1).

Original entry on oeis.org

1, 1, 11, 547, 52429, 8138021, 1865813431, 593445188743, 250199979298361, 135085171767299209, 90909090909090909091, 74619186937936447687211, 73381705110822317661638341, 85180949465178001182799643437, 115244915978498073437814463065839, 179766618030828831251710653305053711

Offset: 0

Martin Saturka (martin(AT)saturka.net), Jul 31 2010

a(n) is the arithmetic mean of the multiset consisting of n lots of 1/n and one lot of n^(2*n+1). This multiset also has an integer valued geometric mean which is equal to n for n > 0.

According to search at OEIS for particular sequence members, a(n) is also: (1+2*n)-th q-integer for q=-n, (2*(n+1))-th cyclotomic polynomial at q=-n, Gaussian binomial coefficient [2*n+1, 2*n] for q=-n, number of walks of length 1+2*n between any two distinct vertices of the complete graph K_(n+1).

			For n = 2, a(2) = 11 which is the arithmetic mean of {1/2, 1/2, 2^5} = 33 / 3 = 11. The geometric mean is 8^(1/3) = 2, i.e. both are integral.

Andrew Howroyd, Table of n, a(n) for n = 0..100
Google Groups, Integer-valued arithmetic and geometric means of sequences with non-integer numbers

Main diagonal of A362783.

Values for n = 5, 6 via other ways. Q-integers: A014986, A014987, K_n paths: A015531, A015540, Cyclotomic polynomials: A020504, A020505, Gaussian binomial coefficients: A015391, A015429.

a(n) = (n^(2*n + 1) + 1)/(n + 1) \\ Andrew Howroyd, May 03 2023

[(n**(2*n+1)+1)//(n+1) for n in range(1,11)]

a(n) = Sum_{i=0..2*n} (-n)^i.

Edited, a(0)=1 prepended and more terms from Andrew Howroyd, May 03 2023

cp's OEIS Frontend

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

A179897 a(n) = (n^(2*n+1) + 1) / (n+1).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Python

Formula

Extensions