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A038179 Result of second stage of sieve of Eratosthenes. 18
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 (list; graph; refs; listen; history; text; internal format)
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

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

LINKS

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

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)

MAPLE

with(numtheory); P:=proc(q) local n;

for n from 1 to q do print((n+1+(-1)^(n+1))*floor(3/(n+1))+6*floor((n-1)/2)+(-1)^n);

od; end: P(10^4); # Paolo P. Lava, Mar 20 2014

MATHEMATICA

Join[{2, 3}, Select[Table[n, {n, 2, 200}], Mod[#, 2] != 0 && Mod[#, 3] != 0 &]] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *)

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 *)

PROG

(PARI) /* The following PARI program applies to generate all terms besides first one: */ j=[]; for(n=0, 1000, if((floor(sqrt(4!*(n+1) + 1))) == ceil(sqrt(4!*(n+1) + 1)), j=concat(j, floor(sqrt(4!*(n+1) + 1))))); j \\ Alexander R. Povolotsky, Sep 09 2008

CROSSREFS

Cf. A004280, A007310, A144065.

Sequence in context: A329147 A048380 A048382 * A192489 A161578 A261271

Adjacent sequences:  A038176 A038177 A038178 * A038180 A038181 A038182

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 11 1999

STATUS

approved

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Last modified November 21 12:28 EST 2019. Contains 329370 sequences. (Running on oeis4.)