A260679 a(n) = n+(17-n)^2.

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

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 prime-generating 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*m-67 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+(17-n)^2, ", "))
(Magma) [n+(17-n)^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^2-n+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