A267781 Expansion of (x*(-14x^6 - 32x^5 + 16x^4 + 30x^3 - x + 14) + 17)/((x-1)^2*(x+1)).

17, 31, 47, 61, 107, 137, 151, 167, 181, 197, 211, 227, 241, 257, 271, 287, 301, 317, 331, 347, 361, 377, 391, 407, 421, 437, 451, 467, 481, 497, 511, 527, 541, 557, 571, 587, 601, 617, 631, 647, 661, 677, 691, 707, 721, 737, 751, 767, 781, 797, 811, 827, 841, 857, 871, 887, 901, 917, 931, 947, 961, 977, 991, 1007

Offset: 1

Author

Mikk Heidemaa, Jan 20 2016

Keywords

• nonn
• easy

Comments

The terms which are primes are the same (p mod 3 = p mod 5) as in A267540 (starting from a(2)=17, their correspondence is verified up to 150000047).

Primes here frequently also have regular intervals and occur mostly in short blocks (consisting of 2-4 primes) rather than singletons, but some blocks can be much longer (e.g., a(1)..a(15) and a(33)..a(43)).

Crossrefs

Cf. A063118, A267540.

Programs

Mathematica

CoefficientList[ Series[(x*(-14x^6 - 32x^5 + 16x^4 + 30x^3 - x + 14) + 17)/((x - 1)^2*(x + 1)), {x, 0, 63}], x] (* Michael De Vlieger, Jan 21 2016 *)(* Or *)
Flatten @Prepend[ Table[(30*n - (-1)^n + 123)/2, {n, 5, 1000}],{17,31,47,61,107}](* Efficient. Mikk Heidemaa, Jan 21 2016 *)

PARI

Vec((x*(-14*x^6-32*x^5+16*x^4+30*x^3-x+14)+17)/((x-1)^2*(x+1)) + O(x^80)) \\ Michel Marcus, Jan 20 2016

Formula

a(n) = (30*n - (-1)^n + 123)/2 for n > 4. - Colin Barker, Jan 21 2016