A197861 Prime divisor of n which appears the fewest times previously in the sequence, with ties to the smaller prime.

2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 2, 13, 7, 5, 2, 17, 3, 19, 5, 7, 11, 23, 3, 5, 13, 3, 7, 29, 2, 31, 2, 11, 17, 7, 3, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 2, 7, 5, 17, 13, 53, 3, 11, 7, 19, 29, 59, 2, 61, 31, 3, 2, 13, 11, 67, 17, 23, 5, 71, 3, 73, 37, 5, 19

Offset

2,1

Links

Table of n, a(n) for n=2..76.

Example

The only prime divisor of 4 is 2, so a(4) = 2.
The prime divisors of 6 are 2 and 3; in the sequence to that point (2,3,2,5), there are two 2's and 1 3, we take the less common one, so a(6) = 3.
The prime divisors of 12 are 2 and 3; these occur equally often in the sequence to that point, so we take the smaller one; a(12)=2.

Prog

(PARI) al(n)={local(ns=vector(primepi(n)), r=vector(n-1), ps);
  for(k=1, n-1,
    ps=factor(k+1)[, 1]~;
    r[k]=ps[1];
    for(j=2, #ps, if(ns[primepi(ps[j])]<ns[primepi(r[k])], r[k]=ps[j]));
    ns[primepi(r[k])]++);
  r}

Crossrefs

Cf. A197862, A006530.

Sequence in context: A346152 A090662 A088387 * A180506 A273283 A359612

Adjacent sequences: A197858 A197859 A197860 * A197862 A197863 A197864

Keyword

nonn

Author

Franklin T. Adams-Watters, Oct 18 2011

Status

approved