

A260679


a(n) = n+(17n)^2.


1



257, 227, 199, 173, 149, 127, 107, 89, 73, 59, 47, 37, 29, 23, 19, 17, 17, 19, 23, 29, 37, 47, 59, 73, 89, 107, 127, 149, 173, 199, 227, 257, 289, 323, 359, 397, 437, 479, 523, 569, 617, 667, 719, 773, 829, 887, 947, 1009, 1073, 1139, 1207, 1277, 1349, 1423, 1499, 1577, 1657
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OFFSET

1,1


COMMENTS

Motivated by the fact that the first 32 terms of this sequence are primes. This has an explanation through Heegener numbers, similar to Euler's primegenerating polynomial (cf. A002837 and related crossrefs).
See also A007635 for the primes in this sequence, A260678 for indices k for which a(k) is composite.
Sequence provides all numbers m for which 4*m67 is a square. [Bruno Berselli, Nov 16 2015]


LINKS

Table of n, a(n) for n=1..57.
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: x*(257  544*x + 289*x^2)/(1  x)^3.


MATHEMATICA

Table[n + (17  n)^2, {n, 70}] (* Vincenzo Librandi, Nov 16 2015 *)
LinearRecurrence[{3, 3, 1}, {257, 227, 199}, 60] (* Harvey P. Dale, May 12 2019 *)


PROG

(PARI) for(n=1, 99, print1(n+(17n)^2, ", "))
(MAGMA) [n+(17n)^2: n in [1..70]]; // Vincenzo Librandi, Nov 16 2015


CROSSREFS

Cf. A007635 (primes in this sequence = primes of the form n^2+n+17).
Cf. A002837 (n^2n+41 is prime), A005846 (primes of form n^2+n+41), A007634 (n^2+n+41 is composite), A097823 (n^2+n+41 is not squarefree).
Sequence in context: A182912 A276233 A252726 * A043676 A296901 A045030
Adjacent sequences: A260676 A260677 A260678 * A260680 A260681 A260682


KEYWORD

nonn,easy


AUTHOR

M. F. Hasler, Nov 15 2015


STATUS

approved



