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 A128473 Numbers of the form 30*k+23 or numbers that cannot be part of a twin prime pair. 2
 23, 53, 83, 113, 143, 173, 203, 233, 263, 293, 323, 353, 383, 413, 443, 473, 503, 533, 563, 593, 623, 653, 683, 713, 743, 773, 803, 833, 863, 893, 923, 953, 983, 1013, 1043, 1073, 1103, 1133, 1163, 1193, 1223, 1253, 1283, 1313, 1343, 1373, 1403, 1433, 1463 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 30*k + 23 -+ 2 is a multiple of 3 or 5 precluding it from being part of a twin prime pair. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Albert van der Horst, Counting Twin Primes Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA From Vincenzo Librandi, Feb 15 2018: (Start) G.f.: x*(23 + 7*x)/(1 - x)^2. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End) MATHEMATICA Range[23, 7000, 30] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *) CoefficientList[Series[(23 + 7 x) / (1 - x)^2, {x, 0, 50}], x] (* Vincenzo Librandi, Feb 15 2018 *) LinearRecurrence[{3, -3, 1}, {23, 53, 83}, 50] (* or *) NestList[#+30&, 23, 50] (* Harvey P. Dale, Sep 11 2019 *) PROG (PARI) g(n) = forstep(x=23, n, 30, print1(x", ")) (Magma) [30*n+23: n in [0..50]] /* or */ I:=[23, 53, 83]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 15 2018 CROSSREFS Subsequence of A110673. Sequence in context: A055782 A338821 A104802 * A132235 A277993 A339188 Adjacent sequences: A128470 A128471 A128472 * A128474 A128475 A128476 KEYWORD nonn,easy AUTHOR Cino Hilliard, May 06 2007 STATUS approved

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Last modified May 24 12:09 EDT 2024. Contains 372773 sequences. (Running on oeis4.)