A364576 Starting from k=1, each subsequent term is the next larger odd k such that A156552(k) < k and the ratio A156552(k)/k is nearer to 1.0 than for any previous k in the sequence.

1, 3, 5, 21, 323, 66297, 139965, 263375, 264845, 528581

Offset

1,2

Comments

All the odd fixed points of map n -> A005940(n) [and its inverse, map n -> A005941(n)] are included in this sequence. This includes both the known odd fixed points, 1, 3 and 5 (see A029747), and any additional hypothetical odd composites that would satisfy the condition n == A005940(n).

This is a subsequence of A364561, so the comments given in A364564 apply also here.

Links

Table of n, a(n) for n=1..10.

Example

       k  A156552(k)    A156552(k)/k  k-(1+A156552(k)) factorization of k
       1:       0         0                0
       3:       2         0.6666667        0
       5:       4         0.8              0
      21:      18         0.8571429        2           (3 * 7)
     323:     320         0.9907121        2           (17 * 19)
   66297:   65714         0.9912062      582           (3 * 7^2 * 11 * 41)
  139965:  139306         0.9952917      658           (3 * 5 * 7 * 31 * 43)
  263375:  262364         0.9961614     1010           (5^3 * 7^2 * 43)
  264845:  264244         0.9977307      600           (5 * 7^2 * 23 * 47)
  528581:  528576         0.9999905        4           (17^2 * 31 * 59).

Crossrefs

Subsequence of A364561.

Cf. A005940, A005941, A029747, A156552.

Cf. also A364551, A364564, A364572.

Sequence in context: A179265 A084253 A153889 * A186751 A280037 A292557

Adjacent sequences: A364573 A364574 A364575 * A364577 A364578 A364579

Keyword

nonn,more

Author

Antti Karttunen, Aug 06 2023

Status

approved