This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A230462 Numbers congruent to {1, 11, 13, 17, 19, or 29} mod 30. 2
 1, 11, 13, 17, 19, 29, 31, 41, 43, 47, 49, 59, 61, 71, 73, 77, 79, 89, 91, 101, 103, 107, 109, 119, 121, 131, 133, 137, 139, 149, 151, 161, 163, 167, 169, 179, 181, 191, 193, 197, 199, 209, 211, 221, 223, 227, 229, 239, 241, 251, 253, 257, 259, 269 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Reduces sieving for all twin primes (A001097) except (3,5) and (5,7) to 6/30 or 20% of natural numbers. This is subset of natural numbers not divisible by 2, 3 or 5 (A007775). Also A128464(n) and A128464(n)+2 interleaved, with a(n) = 1. - Peter Bala, Oct 28 2013 a(2)..a(10) form a block of 9 primes {11, 13, 17, 19, 29, 31, 41, 43, 47}. Up to 3*10^10 there is only one such block which includes 11 primes: {18873497, 18873499, 18873509, 18873511, 18873521, 18873523, 18873527, 18873529, 18873539, 18873541, 18873551}. Do larger such blocks exist? (None found up to 10^11.) - Mikk Heidemaa, Dec 22 2017 LINKS Iain Fox, Table of n, a(n) for n = 1..10000 Gary W. Croft Twin Primes Demystified Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1). FORMULA G.f.: x*(1+10*x+2*x^2+4*x^3+2*x^4+10*x^5+x^6) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Jul 07 2015 From Wesley Ivan Hurt, Jul 22 2016: (Start) a(n) = a(n-1) + a(n-6) - a(n-7) for n>7; a(n) = a(n-6) + 30 for n>6. a(n) = (30*n - 15 - 6*cos(n*Pi/3) + 6*cos(2*n*Pi/3) + 9*cos(n*Pi) + 6*sqrt(3)*sin(n*Pi/3) - 2*sqrt(3)*sin(2*n*Pi/3))/6. a(6k) = 30k-1, a(6k-1) = 30k-11, a(6k-2) = 30k-13, a(6k-3) = 30k-17, a(6k-4) = 30k-19, a(6k-5) = 30k-29. (End) a(n) = 5*n + ceiling(7/79 - ((((14654/4883)^n mod 6) mod 5) + n mod 3 + 1) mod 7). - Mikk Heidemaa, Dec 13 2017 a(n + 6) = a(n) + 30. - David A. Corneth, Jan 15 2018 MAPLE A230462:=n->30*floor(n/6)+[1, 11, 13, 17, 19, 29][(n mod 6)+1]: seq(A230462(n), n=0..100); # Wesley Ivan Hurt, Jul 22 2016 MATHEMATICA LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {1, 11, 13, 17, 19, 29, 31}, 60] (* Harvey P. Dale, Dec 01 2015 *) ParallelCombine[Select[#, MemberQ[{1, 11, 13, 17, 19, 29}, Mod[#, 30]] &] &, Range[10^4]] (* Mikk Heidemaa, Dec 12 2017 *) CoefficientList[ Series[(1 + 10x + 2x^2 + 4x^3 + 2x^4 + 10x^5 + x^6)/((-1 + x)^2 (1 + x + x^2 + x^3 + x^4 + x^5)), {x, 0, 60}], x] (* Robert G. Wilson v, Jan 09 2018 *) PROG (PARI) a(n)=n\6*30+[-1, 1, 11, 13, 17, 19][n%6+1] \\ Charles R Greathouse IV, Oct 29 2013 (PARI) first(n) = Vec(x*(1 + 10*x + 2*x^2 + 4*x^3 + 2*x^4 + 10*x^5 + x^6)/((1 + x)*(1 + x + x^2)*(x^2 - x + 1)*(x - 1)^2) + O(x^(n+1))) \\ Iain Fox, Dec 29 2017 (MAGMA) [n : n in [0..400] | n mod 30 in [1, 11, 13, 17, 19, 29]]; // Wesley Ivan Hurt, Jul 22 2016 CROSSREFS Cf. A001097, A007775, A128464, A132247. Sequence in context: A052259 A103900 A097358 * A215927 A229947 A132247 Adjacent sequences:  A230459 A230460 A230461 * A230463 A230464 A230465 KEYWORD nonn,easy AUTHOR Gary Croft, Oct 20 2013 EXTENSIONS New name and initial term from Omar E. Pol, Oct 27 2013 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 20 02:57 EST 2018. Contains 317371 sequences. (Running on oeis4.)