A331837 Numbers k such that A331694(k) = k.

1, 6, 126, 198, 1433322, 317533782, 386625738, 451240398, 394171702494, 701463692694, 2111238978018

Offset

1,2

Comments

Is this sequence finite?

a(12) > 3*10^12. It appears that if p>43, p+4, and q=(4p^2+18p-1)/21 are 3 primes, then 6*p*(p+4)*q is a term, so the sequence is probably infinite. Terms of this form are a(6), a(10), 27022402862934, 815943210142422,... Other terms, not of this form, are 74704831120974, 76402543308186, 144328894843494,... - Giovanni Resta, Feb 04 2020

Links

Table of n, a(n) for n=1..11.

Rémy Sigrist, Logarithmic line plot of the sequence {e_k} associated to 451240398

Example

For n = 126, we have (with the notations introduced in A331694):
  k   e_k  d_k
  --  ---  ---
   0    0  N/A
   1    1    1
   2    3    2
   3    0    3
   4    6    6
   5   13    7
   6    4    9
   7   18   14
   8    0   18
   9   21   21
  10   63   42
  11    0   63
  12  126  126
- so 126 is a term.

Prog

(PARI) is(n) = my (e=0); fordiv (n, d, if (e>=d, e-=d, e+=d)); e==n

Crossrefs

Cf. A331694.

Sequence in context: A132507 A223112 A224089 * A254544 A268685 A109820

Adjacent sequences: A331834 A331835 A331836 * A331838 A331839 A331840

Keyword

nonn,more

Author

Rémy Sigrist, Jan 28 2020

Extensions

a(9)-a(11) from Giovanni Resta, Feb 04 2020

Status

approved