A251717 a(n) = smallest positive integer k such that A083221(k, n) has at most two prime factors (is a prime or semiprime).

1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 3, 2, 2, 1, 2, 3, 4, 2, 3, 1, 2, 1, 5, 3, 2, 3, 2, 1, 3, 6, 2, 1, 2, 1, 3, 2, 3, 1, 4, 2, 3, 2, 2, 1, 2, 2, 3, 2, 3, 1, 3, 1, 4, 4, 2, 3, 2, 1, 5, 2, 2, 1, 4, 1, 4, 2, 2, 3, 3, 1, 3, 3, 2, 1, 2, 4, 3, 2, 3, 1, 2, 2, 5, 3, 3, 3, 2, 1, 3, 2, 2, 1, 4, 1, 3, 3, 2, 1, 5, 1, 4, 3, 2, 1, 2, 2, 3, 2, 3, 4, 2

Offset: 1

Author

Antti Karttunen, Dec 15 2014

Keywords

• nonn

Comments

Records occur at 1, 4, 8, 26, 32, 39, 238, 462, 1075, 1763, ... with record values 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, ...

New distinct values occur at 1, 4, 8, 26, 32, 39, 238, 306, 462, 1075, 1106, 1763, ... with the values 1, 2, 3, 4, 5, 6, 8, 7, 9, 11, 10, 13, ...

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2518

Crossrefs

Variant: A251718.

The positions of ones: A008578.

Cf. A001222, A083221 (A083140), A251719.

a(n+1) differs from A057217(n-1) for the first time at n=19, where a(20) = 3, while A057217(18) = 4.

Programs

Scheme

(define (A251717 n) (let loop ((i 1)) (if (<= (A001222 (A083221bi i n)) 2) i (loop (+ i 1))))) ;; Code for A083221bi given in A083221.

Formula

For all n, a(n) <= A251718(n) <= A251719(n).