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 A047222 Numbers that are congruent to {0, 2, 3} mod 5. 26
 0, 2, 3, 5, 7, 8, 10, 12, 13, 15, 17, 18, 20, 22, 23, 25, 27, 28, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 47, 48, 50, 52, 53, 55, 57, 58, 60, 62, 63, 65, 67, 68, 70, 72, 73, 75, 77, 78, 80, 82, 83, 85, 87, 88, 90, 92, 93, 95, 97, 98, 100, 102, 103, 105, 107 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sum of a triangle where the top value is 2 and every elementary triangle or triple is required to have the values 1,2,2 (see link below). Compare with A008854 where the triple contains 1,2,2 with 1 at the top. - Craig Knecht, Oct 18 2015 Also, numbers n such that n*(n^2+1)/5 is a nonnegative integer. [Bruno Berselli, Jan 16 2016] Conjecture: Apart from 0, the sequence gives the values for c/6, such that an infinite number of primes, p, result in both p^2-c and p^2+c being positive primes, except when c is a square. When c is square solutions exist for c (both within and outside of the a(n) set), but occur at only a single prime p. See A274609. Other c values with only one prime providing a solution occur when p^2-c=3. See A274610. The only remaining c values with single p solutions are: c=2 (with p=3) and c=6 (with p=5). - Richard R. Forberg, Jun 26 2016 See A047363 for case of p^3 +- c. See A005097 and A177735 for observations on the general case p^q +- c. - Richard R. Forberg, Aug 11 2016 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Craig Knecht, Row sum for the 1,2,2 triangle with 2 at the top. Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1). FORMULA From R. J. Mathar, Oct 18 2008: (Start) G.f.: x^2*(2 + x + 2*x^2)/((1 - x)^2*(1 + x + x^2)). a(n) = A028738(n-2), 1 < n < 16. (End) a(n) = floor((5*n-4)/3). - Gary Detlefs, Oct 28 2011 a(n) = 2*n - 2 - floor(n/3). - Wesley Ivan Hurt, Nov 07 2013 From Wesley Ivan Hurt, Jun 14 2016: (Start) a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. a(n) = (15*n-15-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9. a(3k) = 5k-2, a(3k-1) = 5k-3, a(3k-2) = 5k-5. (End) a(n) = n - 1 + floor((2n-1)/3). - Wesley Ivan Hurt, Dec 27 2016 MAPLE A047222:=n->2*n-2-floor(n/3); seq(A047222(k), k=1..100); # Wesley Ivan Hurt, Nov 07 2013 MATHEMATICA Floor[(Range[5, 305, 5] - 4)/3] (* Vladimir Joseph Stephan Orlovsky, Jan 26 2012 *) Flatten[Table[5n + {0, 2, 3}, {n, 0, 19}]] (* Alonso del Arte, Nov 07 2013 *) LinearRecurrence[{1, 0, 1, -1}, {0, 2, 3, 5}, 100] (* Vincenzo Librandi, Jun 15 2016 *) PROG (PARI) a(n)=(5*n-4)\3 \\ Charles R Greathouse IV, Oct 28 2011 (PARI) concat(0, Vec(x^2*(2+x+2*x^2)/((1-x)^2*(1+x+x^2)) + O(x^100))) \\ Altug Alkan, Oct 26 2015 (MAGMA) [n : n in [0..150] | n mod 5 in [0, 2, 3]]; // Wesley Ivan Hurt, Jun 14 2016 CROSSREFS Cf. A008854, A028738, A047363, A005097. Sequence in context: A062132 A003258 A028738 * A028763 A285977 A186344 Adjacent sequences:  A047219 A047220 A047221 * A047223 A047224 A047225 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified February 22 11:33 EST 2020. Contains 332135 sequences. (Running on oeis4.)