|
|
A373386
|
|
Smallest integer m > 1 such that m == m^m (mod 10^(len(m) + n)), where len(m) is the number of digits of m.
|
|
0
|
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
By definition, this sequence is a subsequence of A082576.
It is not known if a(n) = 10^(n + 1) + 1 holds for all n >= 3.
|
|
LINKS
|
|
|
EXAMPLE
|
a(2) = 751 since m = 751 is the smallest integer satisfying m == m^m (mod 10^(len(m) + 2)), given the fact that 751 is a 3-digit number and 751^751 == 500751 (mod 10^6) and thus 751^751 == 751 (mod 10^(3 + 2)).
|
|
PROG
|
(PARI) a(n) = my(im); for (len_m = 1, oo, if (len_m==1, im=2, im=10^(len_m - 1)); for (m = im, 10^len_m - 1, if (m == Mod(m, 10^(len_m + n))^m, return(m)))); \\ Michel Marcus, Jun 03 2024
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|