login
A069560
Squares in which the k-th significant digit either divides k or is a multiple of k.
2
1, 4, 9, 16, 25, 49, 64, 81, 121, 144, 169, 324, 361, 625, 961, 1369, 1681, 2116, 2916, 4624, 8649, 11664, 12321, 14161, 14641, 51984, 114921, 151321, 214369, 311364, 351649, 1151329, 1252161, 1658944, 7311616, 7354944, 41254929, 41654116
OFFSET
1,2
COMMENTS
If the smallest prime divisor of n is > 7 then the n-th digit is 1.
a(65) if it exists is > 10^50. - Andrew Howroyd, Sep 20 2024
LINKS
EXAMPLE
8649 is a member in which the fourth digit is 8 a multiple of 4, the third one is 6 a multiple of 3, the second one is 4 a multiple of 2 and the least significant digit is 9.
PROG
(PARI) isok(k)={my(d=digits(k)); for(i=1, #d, my(t=d[#d+1-i]); if(!t || (t%i && i%t), return(0))); 1}
for(k=1, 10000, my(x=k^2); if(isok(x), print1(x, ", "))) \\ Andrew Howroyd, Sep 19 2024
(PARI) \\ faster program
B(k)={
local(L=List());
my(v=vector(k, i, select(t->t%i==0||i%t==0, [1..9])));
my(chk(d)=for(i=1, #d, if(!vecsearch(v[i], d[#d+1-i]), return(0))); 1);
my(s=k\2, b=10^s);
my(recurse(i, m)=if(i==s,
for(j=sqrtint(m*b+b\10-1)+1, sqrtint(m*b+b-1), my(t=j^2); if(chk(digits(t%b)), listput(L, t))),
m*=10; foreach(v[i], t, self()(i-1, m+t))
));
recurse(k, 0);
Vec(L);
}
concat(vector(12, k, B(k))) \\ Andrew Howroyd, Sep 19 2024
CROSSREFS
Intersection of A000290 and A069570.
Sequence in context: A065741 A188061 A279456 * A075494 A063735 A056798
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Mar 22 2002
EXTENSIONS
More terms from Sascha Kurz, Mar 23 2002
Offset changed by Andrew Howroyd, Sep 19 2024
STATUS
approved