A192503 Ludic prime numbers.

2, 3, 5, 7, 11, 13, 17, 23, 29, 37, 41, 43, 47, 53, 61, 67, 71, 83, 89, 97, 107, 127, 131, 149, 157, 173, 179, 181, 193, 211, 223, 227, 233, 239, 257, 277, 283, 307, 313, 331, 337, 353, 359, 383, 389, 397, 419, 421, 431, 433, 463, 467, 503, 509, 541, 577

Offset: 1

Author

Reinhard Zumkeller, Jul 05 2011

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A000040 and A003309.

Cf. A010051, A192490.

Cf. A192506 (neither ludic nor prime).

Programs

Haskell

a192503 n = a192503_list !! (n-1)
a192503_list = filter ((== 1) . a010051) a003309_list

Mathematica

a3309[nmax_] := a3309[nmax] = Module[{t = Range[2, nmax], k, r = {1}}, While[Length[t] > 0, k = First[t]; AppendTo[r, k]; t = Drop[t, {1, -1, k}]]; r];
ludicQ[n_, nmax_] /; 1 <= n <= nmax := MemberQ[a3309[nmax], n];
terms = 1000;
f[nmax_] := f[nmax] = Select[Range[nmax], ludicQ[#, nmax] && PrimeQ[#]&] // PadRight[#, terms]&;
f[nmax = terms];
f[nmax = 2 nmax];
While[f[nmax] != f[nmax/2], nmax = 2 nmax];
seq = f[nmax] (* Jean-François Alcover, Dec 10 2021, after Ray Chandler in A003309 *)

PARI

A192503(maxn,bflag=0)={my(Vw=vector(maxn, x, x+1), Vl=Vec([1]), vwn=#Vw,i,vj,L=List());
while(vwn>0, i=Vw[1]; Vl=concat(Vl,[i]);
      Vw=vector((vwn*(i-1))\i,x,Vw[(x*i+i-2)\(i-1)]); vwn=#Vw);
kill(Vw); vwn=#Vl;
for(j=1,vwn, vj=Vl[j]; if(isprime(vj),listput(L,vj))); kill(Vw); vwn=#L;
if(bflag, for(i=1,vwn, print(i," ",L[i]))); if(!bflag, return(Vec(L)));
} \\ Anatoly E. Voevudko, Feb 28 2016

Formula

A010051(a(n))*A192490(a(n)) = 1.