A069557 Squares in which the k-th significant digit either divides k or is a multiple of k. Is 1 only in case k has no other single-digit divisor.

1, 4, 9, 25, 49, 64, 81, 324, 361, 625, 961, 4624, 8649, 7354944

Offset

1,2

Comments

If the smallest prime divisor of n is > 7 only in such case the n-th digit is 1.

a(15) > 10^25 if it exists. - David A. Corneth, May 05 2024

The definition implies that no digit can be zero. - N. J. A. Sloane, May 05 2024

Links

Table of n, a(n) for n=1..14.

David A. Corneth, PARI program

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.

Mathematica

okQ[n_]:=Module[{idn=IntegerDigits[n]}, Count[idn, 0]==0 && And@@Divisible[idn, Range[Length[idn], 1, -1]]]; Select[Range[500]^2, okQ]  (* Harvey P. Dale, Dec 20 2010 *)

Prog

(PARI) \\ See PARI link

Crossrefs

Cf. A052041, A069556, A069560.

Sequence in context: A244557 A063482 A277312 * A230312 A332646 A306043

Adjacent sequences: A069554 A069555 A069556 * A069558 A069559 A069560

Keyword

base,hard,more,nonn,changed

Author

Amarnath Murthy, Mar 22 2002

Extensions

More terms from Sascha Kurz, Mar 23 2002

Offset corrected and a(14) from Sean A. Irvine, May 04 2024

Status

approved