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

1,1

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

Formula

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

Prog

(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

Crossrefs

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

Sequence in context: A143104 A127236 A117947 * A351956 A092152 A350070

Adjacent sequences: A175857 A175858 A175859 * A175861 A175862 A175863

Keyword

nonn

Author

Jaroslav Krizek, Sep 29 2010

Status

approved