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A114962 a(n) = n^2 + 14. 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 (list; graph; refs; listen; history; text; internal format)
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
J. H. E. Cohn, The diophantine equation x^2 + C = y^n, Acta Arithmetica LXV.4 (1993).
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
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

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Last modified March 2 08:59 EST 2024. Contains 370461 sequences. (Running on oeis4.)