A256148 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

Robert Price, Table of n, a(n) for n = 1..733

Bernhard Helmes, Prime sieving on the polynomial f(n)=n^2+n+1.

MATHEMATICA

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

PROG

(PARI) 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

CROSSREFS

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

Sequence in context: A117708 A093431 A243765 * A083520 A336801 A162869

Adjacent sequences: A256145 A256146 A256147 * A256149 A256150 A256151

KEYWORD

nonn,look

AUTHOR

Robert Price, Mar 16 2015

STATUS

approved