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

Author

Jonathan Vos Post, Aug 18 2006

Keywords

• easy
• nonn

Links

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

Crossrefs

Subsequence of A003627.

Cf. A000040, A005658.

Programs

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

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

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

Formula

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

Extensions

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