A069560 Squares in which the k-th significant digit either divides k or is a multiple of k.

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

Author

Amarnath Murthy, Mar 22 2002

Keywords

• base
• nonn

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

Examples

			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.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..64

Crossrefs

Intersection of A000290 and A069570.

Cf. A069556, A069557, A069558, A069559.

Programs

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

Extensions

More terms from Sascha Kurz, Mar 23 2002

Offset changed by Andrew Howroyd, Sep 19 2024