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

1,4

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

Formula

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

Prog

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

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.

Sequence in context: A328026 A326975 A204893 * A057217 A193330 A147810

Adjacent sequences: A251714 A251715 A251716 * A251718 A251719 A251720

Keyword

nonn

Author

Antti Karttunen, Dec 15 2014

Status

approved