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%I #34 Sep 08 2022 08:45:23
%S 22,23,26,31,38,47,58,71,86,103,122,143,166,191,218,247,278,311,346,
%T 383,422,463,506,551,598,647,698,751,806,863,922,983,1046,1111,1178,
%U 1247,1318,1391,1466,1543,1622,1703,1786,1871,1958,2047,2138,2231,2326,2423
%N a(n) = n^2 + 22.
%C Old name was: "Numbers of the form x^2 + 22".
%C x^2 + 22 != y^n for all x,y and n > 1.
%H Vincenzo Librandi, <a href="/A114963/b114963.txt">Table of n, a(n) for n = 0..1000</a>
%H J. H. E. Cohn, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa65/aa6546.pdf">The diophantine equation x^2 + C = y^n</a>, Acta Arithmetica LXV.4 (1993).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: x*(22 - 43*x + 23*x^2)/(1 - x)^3. - _Vincenzo Librandi_, Apr 30 2014
%F From _Amiram Eldar_, Nov 04 2020: (Start)
%F Sum_{n>=0} 1/a(n) = (1 + sqrt(22)*Pi*coth(sqrt(22)*Pi))/44.
%F Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(22)*Pi*cosech(sqrt(22)*Pi))/44. (End)
%t Table[n^2 + 22, {n, 0, 60}] (* _Vincenzo Librandi_, Apr 30 2014 *)
%o (PARI) a(n)=n^2+22 \\ _Amiram Eldar_, Nov 04 2020
%o (Magma) [n^2+22: n in [0..60]]; // _Vincenzo Librandi_, Apr 30 2014
%Y Cf. similar sequences listed in A114962.
%K nonn,easy
%O 0,1
%A _Cino Hilliard_, Feb 21 2006
%E a(0)=22 from _Vincenzo Librandi_, Apr 30 2014
%E Definition changed by _Bruno Berselli_, Mar 13 2015
%E Offset corrected by _Amiram Eldar_, Nov 04 2020
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