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%I #43 Jul 22 2021 23:47:13
%S 17,31,47,61,107,137,151,167,181,197,211,227,241,257,271,287,301,317,
%T 331,347,361,377,391,407,421,437,451,467,481,497,511,527,541,557,571,
%U 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
%N Expansion of (x*(-14x^6 - 32x^5 + 16x^4 + 30x^3 - x + 14) + 17)/((x-1)^2*(x+1)).
%C 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).
%C 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)).
%F a(n) = (30*n - (-1)^n + 123)/2 for n > 4. - _Colin Barker_, Jan 21 2016
%t 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 *)
%t Flatten @Prepend[ Table[(30*n - (-1)^n + 123)/2, {n, 5, 1000}],{17,31,47,61,107}](* Efficient. _Mikk Heidemaa_, Jan 21 2016 *)
%o (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
%Y Cf. A063118, A267540.
%K nonn,easy
%O 1,1
%A _Mikk Heidemaa_, Jan 20 2016
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