A285701 a(n) = number of iterations x -> A064216(x) needed to reach a nonprime number when starting from n, a(2) = a(3) = 1.

0, 1, 1, 0, 1, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0

Offset

1,7

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

If A010051(n) = 0 [when n is a nonprime], a(n) = 0, otherwise a(n) = 1 + a(A064216(n)), with a(2) = a(3) = 1.

Example

For n=2, A064216(2) = 2, thus there is exactly one distinct prime that can be reached when iterating A064216 starting from 2, thus a(2) = 1.
For n=19, A064216(19) = 31 (a prime), A064216(31) = 59 (a prime) and A064216(59) = 44 (not a prime), thus there are exactly three distinct primes that are encountered when iterating A064216 starting from 19 before a nonprime is reached, thus a(19) = 3 (the count includes also the starting prime 19).

Prog

(PARI)
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A064216(n) = A064989((2*n)-1);
A285701(n) = if(!isprime(n), 0, if((2==n)||(3==n), 1, 1+A285701(A064216(n))));
(Scheme)
(definec (A285701 n) (cond ((zero? (A010051 n)) 0) ((or (= 2 n) (= 3 n)) 1) (else (+ 1 (A285701 (A064216 n))))))
;; Another version not requiring A064216 and A064989:
(definec (A285701 n) (cond ((zero? (A010051 n)) 0) ((or (= 2 n) (= 3 n)) 1) ((zero? (A010051 (+ n n -1))) 1) (else (+ 1 (A285701 (A000040 (+ -1 (A000720 (+ n n -1)))))))))

Crossrefs

Cf. A000040, A000720, A010051, A048674, A064216, A064989, A245449, A246373, A285700, A285706.

Cf. A005382 (gives positions of terms > 1 from its third term 7 onward).

Sequence in context: A176917 A302110 A085983 * A088183 A308470 A070140

Adjacent sequences: A285698 A285699 A285700 * A285702 A285703 A285704

Keyword

nonn

Author

Antti Karttunen, Apr 26 2017

Status

approved