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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 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

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