login
This site is supported by donations to The OEIS Foundation.

 

Logo

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A230462 Numbers congruent to {1, 11, 13, 17, 19, 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

LINKS

Table of n, a(n) for n=1..54.

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)

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 *)

PROG

(PARI) a(n)=n\6*30+[-1, 1, 11, 13, 17, 19][n%6+1] \\ Charles R Greathouse IV, Oct 29 2013

(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.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 20 06:32 EDT 2017. Contains 290824 sequences.