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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
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
FORMULA
G.f.: x*(257 - 544*x + 289*x^2)/(1 - x)^3.
From Elmo R. Oliveira, Feb 11 2025: (Start)
E.g.f.: exp(x)*(x^2 - 32*x + 289) - 289.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
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).
Cf. A260678.
Sequence in context: A182912 A276233 A252726 * A043676 A296901 A045030
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Nov 15 2015
STATUS
approved