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 A091998 Numbers that are congruent to {1, 11} mod 12. 17
 1, 11, 13, 23, 25, 35, 37, 47, 49, 59, 61, 71, 73, 83, 85, 95, 97, 107, 109, 119, 121, 131, 133, 143, 145, 155, 157, 167, 169, 179, 181, 191, 193, 203, 205, 215, 217, 227, 229, 239, 241, 251, 253, 263, 265, 275, 277, 287, 289, 299, 301, 311, 313, 323, 325, 335 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Cf. property described by Gary Detlefs in A113801: more generally, these numbers are of the form (2*h*n + (h-4)*(-1)^n-h)/4 (h and n in A000027), then ((2*h*n + (h-4)*(-1)^n - h)/4)^2 - 1 == 0 (mod h); in our case, a(n)^2 - 1 == 0 (mod 12). Also a(n)^2 - 1 == 0 (mod 24). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA a(n) = 12*n - a(n-1) - 12 (with a(1)=1). - Vincenzo Librandi, Nov 16 2010 a(n) = 6*n + 2*(-1)^n - 3. G.f.: x*(1+10*x+x^2)/((1+x)*(1-x)^2). a(n) - a(n-1) - a(n-2) + a(n-3) = 0 for n > 3. a(n) = a(n-2) + 12 for n > 2. a(n) = 12*A000217(n-1) + 1 - 2*Sum_{i=1..n-1} a(i) for n > 1. MATHEMATICA LinearRecurrence[{1, 1, -1}, {1, 11, 13}, 100] (* Harvey P. Dale, Jul 26 2017 *) PROG (MAGMA) [ n: n in [1..350] | n mod 12 eq 1 or n mod 12 eq 11 ]; (Haskell) a091998 n = a091998_list !! (n-1) a091998_list = 1 : 11 : map (+ 12) a091998_list -- Reinhard Zumkeller, Jan 07 2012 (PARI) is(n)=n=n%12; n==11 || n==1 \\ Charles R Greathouse IV, Jul 02 2013 CROSSREFS First row of A092260. Cf. A175885 (n == 1 or 10 (mod 11)), A175886 (n == 1 or 12 (mod 13)). Cf. A097933 (primes), A195143 (partial sums). Cf. A005408, A047209, A007310, A047336, A047522, A056020, A090771, A175887. Sequence in context: A192931 A002367 A160373 * A208296 A289696 A023232 Adjacent sequences:  A091995 A091996 A091997 * A091999 A092000 A092001 KEYWORD nonn,easy AUTHOR Ray Chandler, Feb 21 2004 EXTENSIONS Formulae and comment added by Bruno Berselli, Nov 17 2010 - Nov 18 2010 STATUS approved

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)