A175860 a(n) = characteristic function of numbers k such that A175856(m) = k has solution for any m, where A175856(m): a(m) = m for m = noncomposites, a(m) = previous term - 1 for m = composites.

1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1

Offset: 1

Author

Jaroslav Krizek, Sep 29 2010

Keywords

• nonn

Comments

a(n) = characteristic function of numbers from A175857(n). a(n) = 1 if A175856(m) = n for any m, else 0. a(n) = 1 for such n that A175862(n) >= 1. a(n) = 0 for such n that A175862(n) = 0. a(n) + A175861(n) = A000012(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Wikipedia, Bertrand's postulate (Generalizations)
• Index entries for characteristic functions

Crossrefs

Cf. A175856, A175857, A175858, A175859, A175861, A175862.

Programs

PARI

up_to = 100000;
A175856list(up_to) = { my(v=vector(up_to)); for(n=1,up_to,if((1==n)||isprime(n),v[n] = n,v[n] = v[n-1] - 1)); (v); };
\\ This implementation depends on M. El Bachraoui's proof that there exists a prime between 2n and 3n for n > 1 (see Wikipedia-article).
A175860list(up_to) = { my(v=vector(up_to), A175857 = Set(A175856list(prime(2+primepi(2*up_to))))); for(n=1,up_to,v[n] = (0!=vecsearch(A175857,n))); (v); };
v175860 = A175860list(up_to);
A175860(n) = v175860[n]; \\ Antti Karttunen, Nov 08 2018

Formula

a(n) = 1 - A175861(n).