OFFSET
0,1
COMMENTS
a(n) <= max(2, n) for any n >= 0.
a(n*a(n)) <= a(n) for any n >= 0 (see also A283927).
a(n) = 2 iff n belongs to A062846.
Conjecture: if n is composite, then a(n) < n (see also A283937).
Theorem: If n is composite, then a(n) < n. Proof: If n=ab with 1<a<b, then n_b=a0, which interpreted as ab^2 is a multiple of n; if n=b^2 then n_b=100, which interpreted as b^4 is again a multiple of n. - Michael R Peake, Mar 25 2017
First occurrence of b > 1: 1, 4, 13, 6, 31, 36, 41, 46, 71, 12, 133, 53, 155, 106, 161, 18, 199, 20, 261, ..., . - Robert G. Wilson v, Mar 19 2017
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..10000
EXAMPLE
The number 5, when expressed in base 2 and then interpreted in base 4, yields 17, not a multiple of 5.
The number 5, when expressed in base 3 and then interpreted in base 9, yields 11, not a multiple of 5.
The number 5, when expressed in base 4 and then interpreted in base 16, yields 17, not a multiple of 5.
The number 5, when expressed in base 5 and then interpreted in base 25, yields 25, a multiple of 5.
Hence, a(5)=5.
MATHEMATICA
f[n_] := Block[{b = 2}, While[ Mod[ FromDigits[ IntegerDigits[n, b], b^2], n] > 0, b++]; b]; Array[f, 80, 0] (* Robert G. Wilson v, Mar 19 2017 *)
PROG
(PARI) a(n) = my (b=2); if (n>0, while (fromdigits(digits(n, b), b^2)%n, b++)); return (b)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 15 2017
STATUS
approved