This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A051062 a(n) = 16*n + 8. 13
 8, 24, 40, 56, 72, 88, 104, 120, 136, 152, 168, 184, 200, 216, 232, 248, 264, 280, 296, 312, 328, 344, 360, 376, 392, 408, 424, 440, 456, 472, 488, 504, 520, 536, 552, 568, 584, 600, 616, 632, 648, 664, 680, 696, 712, 728, 744, 760, 776, 792, 808, 824, 840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0(97). n such that 32 is the largest power of 2 dividing A003629(k)^n-1 for any k. - Benoit Cloitre, Mar 23 2002 Continued fraction expansion of tanh(1/8). - Benoit Cloitre, Dec 17 2002 If Y and Z are 2-blocks of a (4n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting both Y and Z. - Milan Janjic, Oct 28 2007 General form: (q*n+x)*q x=+1; q=2=A016825, q=3=A017197, q=4=A119413, ... x=-1; q=3=A017233, q=4=A098502, ... x=+2; q=4=A051062, ... - Vladimir Joseph Stephan Orlovsky, Feb 16 2009 A003484(a(n)) = 8; A209675(a(n)) = 9. - Reinhard Zumkeller, Mar 11 2012 A007814(a(n)) = 3; A037227(a(n)) = 7. - Reinhard Zumkeller, Jun 30 2012 a(n)*n+1 = (4n+1)^2 and a(n)*(n+1)+1 = (4n+3)^2 are both perfect squares. - Carmine Suriano, Jun 01 2014 For all positive integers n, there are infinitely many positive integers k such that k*n + 1 and k*(n+1) + 1 are both perfect squares. Except for 8, all the numbers of this sequence are the smallest integers k which are solutions for getting two perfect squares. Example: a(1) = 24 and 24 * 1 + 1 = 25 = 5^2, then 24 * (1+1) + 1 = 49 = 7^2. [Reference AMM] - Bernard Schott, Sep 24 2017 Numbers k such that 3^k + 1 is divisible by 17*193. - Bruno Berselli, Aug 22 2018 Numbers that have three times as many even divisors as odd divisors. - Paolo P. Lava, Oct 17 2018 REFERENCES Letter from Gary W. Adamson concerning Prouhet-Thue-Morse sequence, Nov 11 1999 LINKS Mihaly Bencze, Problem 11508, The American Mathematical Monthly, Vol. 117, N° 5, May 2010, p. 459. Milan Janjic, Two Enumerative Functions Tanya Khovanova, Recursive Sequences William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N)) William A. Stein, The modular forms database Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA a(n) = A118413(n+1,4) for n>3. - Reinhard Zumkeller, Apr 27 2006 a(n) = 32*n - a(n-1) for n>0, a(0)=8. - Vincenzo Librandi, Aug 06 2010 a(-1 - n) = - a(n). - Michael Somos, Jun 02 2014 a(n) = 2*A017113(n) - Paolo P. Lava, Oct 17 2018 MAPLE A051062:=n->16*n+8; seq(A051062(n), n=0..50); # Wesley Ivan Hurt, Jun 01 2014 MATHEMATICA Range[8, 1000, 16] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *) Table[16n+8, {n, 0, 50}] (* Wesley Ivan Hurt, Jun 01 2014 *) LinearRecurrence[{2, -1}, {8, 24}, 60] (* or *) NestList[#+16&, 8, 60] (* Harvey P. Dale, Aug 18 2019 *) PROG (MAGMA) [16*n+8: n in [0..50]]; // Wesley Ivan Hurt, Jun 01 2014 (PARI) a(n)=16*n+8 \\ Charles R Greathouse IV, May 09 2016 CROSSREFS Cf. A008598, A119413, A106839, A017113. Sequence in context: A050427 A031046 A173080 * A152531 A074348 A063403 Adjacent sequences:  A051059 A051060 A051061 * A051063 A051064 A051065 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Gary W. Adamson, Dec 11 1999 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 16 19:17 EST 2019. Contains 329201 sequences. (Running on oeis4.)