A256146 -id:A256146 - cp's OEIS frontend

A256148 Primitive prime factors of the cyclotomic polynomial sequence Phi(3, k) (or Phi(6, k)) in the order in which they occur.

3, 7, 13, 31, 43, 19, 73, 37, 157, 61, 211, 241, 307, 127, 421, 463, 79, 601, 757, 271, 67, 331, 151, 1123, 397, 97, 1483, 223, 547, 1723, 139, 631, 283, 109, 103, 181, 2551, 379, 919, 409, 2971, 3307, 163, 3541, 523, 3907, 613, 4423, 4831, 1657, 5113, 751

Offset: 1

Robert Price, Mar 16 2015

Phi(3,k) = k^2 + k + 1 and Phi(6,k) = k^2 - k + 1.
Interesting scatter plot.
The terms correspond to the new primes of A081257 in the order of their appearance for n>1 and when A081257(m)>m. - Bill McEachen, Oct 13 2022

Robert Price, Table of n, a(n) for n = 1..733
Bernhard Helmes, Prime sieving on the polynomial f(n)=n^2+n+1.

Cf. A005529, A248874, A256144, A256145, A256146, A081257.

prim = {}; Do[prim = Join[prim, Complement[First /@ FactorInteger[Cyclotomic[6, k]], prim]], {k, 1000}]; prim

lista(nn) = {vs = []; for (n=1, nn, vp = factor(polcyclo(6,n))[,1]; for (i=1, #vp, if (!vecsearch(vs, vp[i]), print1(vp[i], ", "); vs = vecsort(concat(vs, vp[i]),,8););););} \\ Michel Marcus, Mar 20 2015

A256153 Primitive prime factors of the cyclotomic polynomial sequence Phi(5,k) in the order in which they occur.

Original entry on oeis.org

5, 31, 11, 71, 311, 2801, 151, 61, 41, 271, 3221, 22621, 30941, 3761, 4931, 88741, 2711, 911, 251, 40841, 245411, 292561, 346201, 521, 8641, 4561, 637421, 732541, 837931, 17351, 601, 1801, 39451, 22571, 49831, 101, 4271, 194681, 191, 401, 2625641, 579281

Offset: 1

Robert Price, Mar 16 2015

nonn

Phi(5,k) = k^4 + k^3 + k^2 + k + 1.

All terms end with the digit 1.

Robert Price, Table of n, a(n) for n = 1..1191

Cf. A005529, A248874, A256144, A256145, A256146, A256148.

prim = {}; Do[prim = Join[prim, Complement[First /@ FactorInteger[Cyclotomic[5, k]], prim]], {k, 1000}]; prim

lista(nn) = {vs = []; for (n=1, nn, vp = factor(polcyclo(5,n))[,1]; for (i=1, #vp, if (!vecsearch(vs, vp[i]), print1(vp[i], ", "); vs = vecsort(concat(vs, vp[i]),,8););););} \\ Michel Marcus, Mar 20 2015

cp's OEIS Frontend

A256148 Primitive prime factors of the cyclotomic polynomial sequence Phi(3, k) (or Phi(6, k)) in the order in which they occur.

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