login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A068165
Smallest square formed from n by inserting zero or more decimal digits.
9
1, 25, 36, 4, 25, 16, 576, 81, 9, 100, 121, 121, 1369, 144, 1156, 16, 1764, 1089, 169, 2025, 121, 225, 2304, 324, 25, 256, 2704, 289, 289, 2304, 361, 324, 3136, 324, 3025, 36, 3721, 3481, 1369, 400, 441, 4225, 4356, 144, 4225, 4096, 4761, 484, 49, 2500
OFFSET
1,2
COMMENTS
The digits may be added before, in the middle of, or after the digits of n.
If n is a square then a(n) = n. - Zak Seidov, Nov 13 2014
LINKS
EXAMPLE
Smallest square formed from 20 is 2025, by placing 25 on the right side. Smallest square formed from 33 is 3136, by inserting a 1 between 3's and placing a 6.
MAPLE
A068165 := proc(n)
local b, pdigs, plen, dmas, dmasdigs, i, j;
for b from 1 do
pdigs := convert(b^2, base, 10) ;
plen := nops(pdigs) ;
for dmas from 2^plen-1 to 0 by -1 do
dmasdigs := convert(dmas, base, 2) ;
pdel := [] ;
for i from 1 to nops(dmasdigs) do
if op(i, dmasdigs) = 1 then
pdel := [op(pdel), op(i, pdigs)] ;
end if;
end do:
if n = add(op(j, pdel)*10^(j-1), j=1..nops(pdel)) then
return b^2;
end if;
end do:
end do:
end proc:
seq(A068165(n), n=1..133) ; # R. J. Mathar, Nov 14 2014
PROG
(Python)
from math import isqrt
from itertools import count
def dmo(n, t):
if t < n: return False
while n and t:
if n%10 == t%10:
n //= 10
t //= 10
return n == 0
def a(n):
return next(t for t in (i*i for i in count(isqrt(n))) if dmo(n, t))
print([a(n) for n in range(1, 77)]) # Michael S. Branicky, Jan 21 2023
CROSSREFS
A091873 gives square roots. Cf. A038690, A029944, A068164.
Sequence in context: A243749 A331143 A031366 * A086935 A077689 A018796
KEYWORD
base,easy,nonn
AUTHOR
Amarnath Murthy, Feb 25 2002
EXTENSIONS
Corrected and extended by Ray Chandler, Oct 11 2003
STATUS
approved