A192504 Ludic nonprime numbers.

1, 25, 77, 91, 115, 119, 121, 143, 161, 175, 209, 221, 235, 247, 265, 287, 301, 329, 341, 361, 377, 407, 415, 437, 445, 475, 481, 493, 497, 517, 527, 535, 553, 565, 581, 595, 625, 667, 685, 697, 703, 707, 749, 775, 791, 803, 805, 835, 841, 851, 865, 893, 913

Offset: 1

Author

Reinhard Zumkeller, Jul 05 2011

Keywords

• nonn

Comments

The sequence appears to have linear growth with ratio a(n)/n ~ 1.73... - M. F. Hasler, Nov 04 2024

Links

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

Crossrefs

Intersection of A018252 and A003309.

Cf. A010051, A192490.

Cf. A002808.

Programs

Haskell

a192504 n = a192504_list !! (n-1)
a192504_list = filter ((== 0) . 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

A192504(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))*(1-A192490(a(n))) = 1.