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

1,2

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

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

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.

Cf. A069556, A069557, A069558, A069559.

Sequence in context: A065741 A188061 A279456 * A075494 A063735 A056798

Adjacent sequences: A069557 A069558 A069559 * A069561 A069562 A069563

Keyword

base,nonn,changed

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