|
| |
|
|
A338371
|
|
Integers for which there exists a self-repetition that is a term of A338166.
|
|
0
|
|
|
|
13, 17, 18, 19, 26, 31, 37, 39, 48, 49, 56, 62, 65, 71, 73, 79, 81, 84, 91, 93, 94, 97, 103
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
18 is a term since 1818 is a term of A338166.
48 is a term since 484848 is a term of A338166.
List of terms with their minimum number of repetitions : [13, 15], [17, 280], [18, 2], [19, 819], [26, 15], [31, 15], [37, 12], [39, 15], [48, 3], [49, 3243], [56, 3], [62, 15], [65, 3], [71, 280], [73, 12], [79, 624], [81, 2], [84, 3], [91, 819], [93, 15], [94, 3243], [97, 624], [103, 10234].
|
|
|
PROG
|
(PARI) f(n) = my(f=factor(n)); vecsum(f[, 1]) + sum(k=1, #f~, if (f[k, 2]!=1, f[k, 2])); \\ A338038
period(vp, n) = {my(p = 1, pten = 10^#Str(n)); for (i=1, #vp, if ((vp[i] != 2) && (vp[i] != 5), p = lcm(p, znorder(Mod(pten, vp[i]))); p = lcm(p, znorder(Mod(pten, vp[i]^2))); ); ); p; }
isok(n) = {my(r = fromdigits(Vecrev(digits(n)))); my(vp = setunion(factor(n)[, 1]~, factor(r)[, 1]~)); my(nbmax = period(vp, n)); if (nbmax == 1, nbmax = 2); my(krep=1); my(pten = 10^#Str(n)); for (k=2, nbmax, krep = pten*krep+1; my(q=1); for (i=1, #vp, my(va = valuation(krep, vp[i])); q *= vp[i]^va; ); if (f(n*q) == f(r*q), return(k); ); ); }
ispal(n) = my(d=Vecrev(digits(n))); n == fromdigits(d);
lista(nn) = {for (n=1, nn, if ((n % 10) && !ispal(n), if (isok(n), print1(n, ", ")); ); ); }
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base,more
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
