This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A260679 #23 Feb 17 2025 22:38:02
%S A260679 257,227,199,173,149,127,107,89,73,59,47,37,29,23,19,17,17,19,23,29,
%T A260679 37,47,59,73,89,107,127,149,173,199,227,257,289,323,359,397,437,479,
%U A260679 523,569,617,667,719,773,829,887,947,1009,1073,1139,1207,1277,1349,1423,1499,1577,1657
%N A260679 a(n) = n + (17 - n)^2.
%C A260679 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).
%C A260679 See also A007635 for the primes in this sequence, A260678 for indices k for which a(k) is composite.
%C A260679 Sequence provides all numbers m for which 4*m - 67 is a square. - _Bruno Berselli_, Nov 16 2015
%H A260679 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A260679 G.f.: x*(257 - 544*x + 289*x^2)/(1 - x)^3.
%F A260679 From _Elmo R. Oliveira_, Feb 11 2025: (Start)
%F A260679 E.g.f.: exp(x)*(x^2 - 32*x + 289) - 289.
%F A260679 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t A260679 Table[n + (17 - n)^2, {n, 70}] (* _Vincenzo Librandi_, Nov 16 2015 *)
%t A260679 LinearRecurrence[{3,-3,1},{257,227,199},60] (* _Harvey P. Dale_, May 12 2019 *)
%o A260679 (PARI) for(n=1,99,print1(n+(17-n)^2,","))
%o A260679 (Magma) [n+(17-n)^2: n in [1..70]]; // _Vincenzo Librandi_, Nov 16 2015
%Y A260679 Cf. A007635 (primes in this sequence = primes of the form n^2 + n + 17).
%Y A260679 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).
%Y A260679 Cf. A260678.
%K A260679 nonn,easy
%O A260679 1,1
%A A260679 _M. F. Hasler_, Nov 15 2015