A120847 Klarner-Rado primes. Primes in A005658.

2, 5, 17, 29, 47, 53, 83, 89, 101, 173, 191, 251, 263, 269, 281, 317, 431, 467, 479, 521, 587, 659, 809, 857, 911, 929, 947, 953, 983, 1019, 1091, 1163, 1307, 1439, 1451, 1493, 1559, 1601, 1613, 1667, 1811, 1847, 1871, 1901, 1979, 2027, 2063, 2099, 2207, 2243

Offset

1,1

Links

R. J. Mathar and Robert Israel, Table of n, a(n) for n = 1..7948 (1..493 from Mathar)

Formula

A000040 INTERSECTION {sequence starting with 1 and such that if n appears so do 2n, 3n+2, 6n+3}.

Maple

N:= 3000: # to get all terms <= N
A:= Vector(N):
A[1]:= 1:
todo:= {1}:
while todo <> {} do
x:= todo[1];
todo:= todo[2..-1];
Y:= select(t -> (t <= N and A[t] = 0), [2*x, 3*x+2, 6*x+3]);
  A[Y]:= 1;
  todo:= todo union convert(Y, set);
od:
select(t -> A[t]=1 and isprime(t), [$1..N]); # Robert Israel, Jun 17 2015

Prog

(C++) #include <stdio.h> #include <iostream> #include <set> using namespace std ; bool isprime(const int n) { for(int i=2; i*i <= n ; i++) if( n %i == 0) return false ; return true ; } int main(int argc, char *argv[]) { const int anmax= 40000 ; set<int> a ; a.insert(1) ; for(int i=0; i< anmax ; i++) { if( a.count(i) ) { if( 2*i<=anmax) a.insert(2*i) ; if( 3*i+2 <= anmax) a.insert(3*i+2) ; if( 6*i+3 <= anmax) a.insert(6*i+3) ; } } int n=1 ; for(int i=2; i < anmax; i++) { if( a.count(i) && isprime(i) ) { cout << n << " " << i << endl ; n++ ; } } return 0 ; } /* R. J. Mathar, Aug 20 2006 */
(MATLAB)
N = 10^4;
A = zeros(1, N);
todo = [1];
A(1) = 1;
while numel(todo) > 0
  x = todo(1);
  todo = todo(2:end);
  Y = [2*x, 3*x+2, 6*x+3];
  Y = Y(Y <= N);
  Y = Y(A(Y) == 0);
  A(Y) = 1;
  todo = [todo, Y];
end;
S = find(A==1);
S(isprime(S)) % Robert Israel, Jun 17 2015
(PARI) has(n)=if(n<3, return(n>0)); my(k=n%6); if(k==3, return(has(n\6))); if(k==1, return(0)); if(k==5, return(has(n\3))); if(k!=2, return(has(n/2))); has(n\3) || has(n/2)
print1(2); forprime(p=5, 1e5, if(p%3==2 && has(p\3), print1(", "p))) \\ Charles R Greathouse IV, Sep 15 2015

Crossrefs

Subsequence of A003627.

Cf. A000040, A005658.

Sequence in context: A243183 A195271 A077217 * A244085 A019353 A106882

Adjacent sequences: A120844 A120845 A120846 * A120848 A120849 A120850

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 18 2006

Extensions

More terms from R. J. Mathar, Aug 20 2006

Status

approved