A257689 Numbers that are either ludic or prime.

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 115, 119, 121, 127, 131, 137, 139, 143, 149, 151, 157, 161, 163, 167, 173, 175, 179, 181, 191, 193, 197, 199, 209, 211, 221, 223, 227, 229, 233, 235, 239, 241, 247, 251, 257, 263, 265

Offset: 1

Author

Antti Karttunen, May 07 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10181

Crossrefs

Union of primes (A000040) and ludic numbers (A003309).

Cf. A192506 (complement, neither ludic nor prime), A192503 (ludic and prime), A192504 (ludic and nonprime), A192505 (nonludic and prime).

Differs from A206074(n-1), A186891(n) and A257688(n) for the first time at n=19, where a(19) = 59, while A206074(18) = A186891(19) = A257688(19) = 55, a term missing from here.

Differs from A257691 for the first time at n=24, where a(24) = 77, while A257691(24) = 79.

Programs

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 *)