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Numbers k such that A331694(k) = k.
1

%I #9 Feb 05 2020 09:45:40

%S 1,6,126,198,1433322,317533782,386625738,451240398,394171702494,

%T 701463692694,2111238978018

%N Numbers k such that A331694(k) = k.

%C Is this sequence finite?

%C 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

%H Rémy Sigrist, <a href="/A331837/a331837.png">Logarithmic line plot of the sequence {e_k} associated to 451240398</a>

%e For n = 126, we have (with the notations introduced in A331694):

%e k e_k d_k

%e -- --- ---

%e 0 0 N/A

%e 1 1 1

%e 2 3 2

%e 3 0 3

%e 4 6 6

%e 5 13 7

%e 6 4 9

%e 7 18 14

%e 8 0 18

%e 9 21 21

%e 10 63 42

%e 11 0 63

%e 12 126 126

%e - so 126 is a term.

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

%Y Cf. A331694.

%K nonn,more

%O 1,2

%A _Rémy Sigrist_, Jan 28 2020

%E a(9)-a(11) from _Giovanni Resta_, Feb 04 2020