A109688 Smallest square that contains exactly n occurrences of the string n.

1, 1, 225, 343396, 44944, 505575225, 4666665969, 77770707876, 388888184881, 9499999990849, 1010101019780101025109910101001, 1101191170117113111111301111961124, 121214127521273511212121212512121241, 135131321313113136131313387213513731136

Offset

0,3

Comments

Occurrences are counted without overlap, so 1111 has two occurrences of 11, not 3. - Michael S. Branicky, Aug 12 2023

Links

Bert Dobbelaere, Table of n, a(n) for n = 0..15

Example

a(2)=225=15^2 since this is the first square that contains two 2's.

Mathematica

With[{sqs=Range[0, 3100000]^2}, Flatten[Table[Select[sqs, DigitCount[#, 10, n] == n&, 1], {n, 9}]]] (* Harvey P. Dale, May 04 2012 *)

Prog

(Python)
from math import isqrt
def a(n):
    sn = str(n)
    k = 1 if n == 0 else isqrt(int(sn*n))
    while True:
        if str(k*k).count(sn) == n:
            return k*k
        k += 1
print([a(n) for n in range(10)]) # Michael S. Branicky, Feb 02 2022

Crossrefs

Sequence in context: A171109 A239478 A304314 * A195277 A319944 A013757

Adjacent sequences: A109685 A109686 A109687 * A109689 A109690 A109691

Keyword

nonn,base

Author

Erich Friedman, Aug 07 2005

Extensions

Corrected and extended by Giovanni Resta, Apr 05 2006

a(10) and beyond from Bert Dobbelaere, Sep 05 2023

Status

approved