A114962 a(n) = n^2 + 14.

14, 15, 18, 23, 30, 39, 50, 63, 78, 95, 114, 135, 158, 183, 210, 239, 270, 303, 338, 375, 414, 455, 498, 543, 590, 639, 690, 743, 798, 855, 914, 975, 1038, 1103, 1170, 1239, 1310, 1383, 1458, 1535, 1614, 1695, 1778, 1863, 1950, 2039, 2130, 2223, 2318, 2415, 2514

Offset

0,1

Comments

Old name was: "Numbers of the form x^2 + 14".

x^2 + 14 != y^n for all x,y and n > 1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

J. H. E. Cohn, The diophantine equation x^2 + C = y^n, Acta Arithmetica LXV.4 (1993).

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: x*(14-27*x+15*x^2)/(1-x)^3. - Colin Barker, Jan 11 2012

From Amiram Eldar, Nov 02 2020: (Start)

Sum_{n>=0} 1/a(n) = (1 + sqrt(14)*Pi*coth(sqrt(14)*Pi))/28.

Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(14)*Pi*cosech(sqrt(14)*Pi))/28. (End)

Mathematica

Table[n^2 + 14, {n, 0, 50}]  (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *)
CoefficientList[Series[(14 - 27 x + 15 x^2)/(1 - x)^3, {x, 0, 80}], x] (* Vincenzo Librandi, Apr 30 2014 *)

Prog

(Magma) [n^2+14: n in [0..60]]; // Vincenzo Librandi, Apr 30 2014

Crossrefs

Cf. A155136, n^2 - 28; A000290, n^2; A114948, n^2 + 10.

Cf. sequences of the type n^2 + k: A002522 (k=1), A059100 (k=2), A117950 (k=3), A087475 (k=4), A117951 (k=5), A114949 (k=6), A117619 (k=7), A189833 (k=8), A189834 (k=9), A114948 (k=10), A189836 (k=11), A241748 (k=12), A241749 (k=13), this sequence (k=14), A241750 (k=15), A241751 (k=16), A241847 (k=17), A241848 (k=18), A241849 (k=19), A241850 (k=20), A241851 (k=21), A114963 (k=22), A241889 (k=23), A241890 (k=24), A114964 (k=30).

Sequence in context: A308974 A130687 A173687 * A278979 A220671 A136012

Adjacent sequences: A114959 A114960 A114961 * A114963 A114964 A114965

Keyword

nonn,easy

Author

Cino Hilliard, Feb 21 2006

Extensions

Added 14 from Vincenzo Librandi, Apr 30 2014

Definition changed by Bruno Berselli, Mar 13 2015

Offset corrected by Amiram Eldar, Nov 02 2020

Status

approved