A292114 List of numbers n such that A039655(n) reaches a new record high.

2, 4, 9, 121, 301, 441, 468, 3171, 8373, 13440, 16641, 16804, 83161, 100652, 133200, 367428, 395640, 459680, 701823, 3739690, 4238314, 6698616, 9014248, 12301860, 16956850, 22230514, 54889200, 60676144, 84983056, 116648892, 128942664

Offset: 1

Author

N. J. A. Sloane, Sep 22 2017

Keywords

• nonn

Comments

Naively, one might have expected these numbers to have some other distinguishing property (primorials, perhaps), but that seems not to be the case.

Increasingly many of the values are of the form m*p with a (large) prime p and a smooth m, often m = 2^k (for a(n), n = 12, 14, 21, 23, 26, 28, 29, ...) or m = 2^k*3^k' (n = 7, 9, 19, 22, 30, ...) or m = 2^k*5^k' (n = 20, 25, ...). I conjecture that almost all terms are even. Also, for most terms (n = 1, 2, 3, 4, 5, 7, 10, 12, 14, 15, 16, 17, 19, 20, 21, 23, 24, 25, 26, 29, 30, 31, ...), either a(n)-1 or a(n)+1 has at most 2 prime divisors. - M. F. Hasler, Sep 25 2017

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..48
• N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)

Crossrefs

Cf. A039654, A039655, A292115.

Programs

PARI

m=-n=1;until(print1(n","),until(A039655(n++)>m,);m=A039655(n)) \\ M. F. Hasler, Sep 25 2017

Extensions

More terms from Hugo Pfoertner, Sep 22 2017