A038179 Result of second stage of sieve of Eratosthenes (after eliminating multiples of 2 and 3).

2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 121, 125, 127, 131, 133, 137, 139, 143, 145, 149, 151

Offset

1,1

Comments

2, 3 and numbers of the form 6m +- 1.

Apart from first two terms, same as A007310.

Terms of this sequence (starting from the third term) are equal to the result of the expression sqrt(4!*(k+1) + 1) - but only when this expression yields integral values (that is when the parameter k takes values, which are terms of A144065). - Alexander R. Povolotsky, Sep 09 2008

References

Fred S. Roberts, Applied Combinatorics, Prentice-Hall, 1984, p. 256.

Links

G. C. Greubel, Table of n, a(n) for n = 1..2500

Ahmed Hamdy A. Diab, Sequence eliminating law (SEL) and the interval formulas of prime numbers, arXiv:2012.03052 [math.NT], 2020.

H. B. Meyer, Eratosthenes' sieve.

Index entries for sequences generated by sieves.

Formula

O.g.f.: x*(2 + x + x^3 + 2x^4)/((1+x)*(1-x)^2). - R. J. Mathar, May 23 2008

a(n) = (1/9)*(4*n^3 + 3*n^2 + 1 - Kronecker(-3,n+1)). - Ralf Stephan, Jun 01 2014

From Mikk Heidemaa, Oct 28 2017: (Start)

a(n) = floor((41/21 - (3 mod n))^(-3*n+5)) + 3*n - 4 (n > 0).

a(n+1) = 3*n - ((n mod 2)+1) mod n (n > 0). (End)

a(n+2) = 2*floor((3*n+1)/2) + 1 for n>=1; see (17) in Diab link. - Michel Marcus, Dec 14 2020

Sum_{n>=1} (-1)^(n+1)/a(n) = (7-sqrt(3)*Pi)/6. - Amiram Eldar, Sep 22 2022

Mathematica

max = 200; Complement[Range[2, max], 2Range[2, Ceiling[max/2]], 6Range[2, Ceiling[max/6]] + 3] (* Alonso del Arte, May 16 2014 *)
Prepend[Table[3*n - Mod[ Mod[n, 2] + 1, n], {n, 1, 999}], 2] (* Mikk Heidemaa, Nov 02 2017 *)

Crossrefs

Cf. A004280, A007310, A144065.

Sequence in context: A048380 A048382 A352584 * A192489 A161578 A261271

Adjacent sequences: A038176 A038177 A038178 * A038180 A038181 A038182

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 1999

Extensions

Name edited by Michel Marcus, Dec 14 2020

Status

approved