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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 *)

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: A113912 A055782 A104802 * A132235 A277993 A051650

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 November 15 01:39 EST 2018. Contains 317224 sequences. (Running on oeis4.)