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A260679 a(n) = n+(17-n)^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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)