A192506 Numbers that are neither ludic nor prime.

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94

Offset: 1

Author

Reinhard Zumkeller, Jul 05 2011

Keywords

• nonn

Comments

Intersection of A002808 and A192607; (1-A010051(a(n)))*(1-A192490(a(n)))=1;

a(n) = A091212(n) for n <= 60.

a(n) = A175526(n) for n <= 53. - Reinhard Zumkeller, Jul 12 2011

In other words, composite numbers that are nonludic. - Antti Karttunen, May 11 2015

Links

• Reinhard Zumkeller (first 1000 terms) & Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A257689 (complement, either ludic or prime), A192503 (ludic and prime), A192504 (ludic and nonprime), A192505 (nonludic and prime).

Cf. A010051, A192490, A002808, A192607.

a(n) differs from A091212(n) and A205783(n+1) for the first time at n=37, where a(37) = 55, while 55 is missing from both A091212 and A205783.

Differs from A175526 for the first time at n=54, where a(54) = 78, while A175526(54) = 77, a term which is missing from here.

Programs

Haskell

a192506 n = a192506_list !! (n-1)
a192506_list = filter ((== 0) . a010051) a192607_list
(Scheme, with Antti Karttunen's IntSeq-library)
(define A192506 (MATCHING-POS 1 1 (lambda (n) (and (zero? (A192490 n)) (zero? (A010051 n))))))
;; Antti Karttunen, May 07 2015

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 *)