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A018796 Smallest square that begins with n. 18
0, 1, 25, 36, 4, 529, 64, 729, 81, 9, 100, 1156, 121, 1369, 144, 1521, 16, 1764, 1849, 196, 2025, 2116, 225, 2304, 2401, 25, 2601, 2704, 289, 2916, 3025, 3136, 324, 3364, 3481, 35344, 36, 3721, 3844, 3969, 400, 41209, 4225, 4356, 441, 45369, 4624, 4761, 484, 49 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
If 4*(n+1) < 10^d then a(n) < (n+1)*10^d. - Robert Israel, Aug 01 2014
LINKS
Zak Seidov, Table of n, a(n) for n = 0..100000 (first 10000 terms from Chai Wah Wu)
EXAMPLE
Among the first 100001 terms, the largest is a(99999) = 99999515529 = 316227^2. - Zak Seidov, May 22 2016
MAPLE
a:= proc(n) local k, d, x;
if issqr(n) then return n
else for d from 1 do
for k from 0 to 10^d-1 do
x:= 10^d*n+k;
if issqr(x) then return x fi
od
od
fi
end proc:
seq(a(n), n=1..100); # Robert Israel, Jul 31 2014
MATHEMATICA
Table[With[{d = IntegerDigits@ n}, k = 1; While[Or[IntegerLength[k^2] < Length@ d, Take[IntegerDigits[k^2], Length@ d] != d], k++]; k^2], {n, 49}] (* Michael De Vlieger, May 23 2016 *)
PROG
(Python)
n = 1
while n < 100:
for k in range(10**3):
if str(k**2).startswith(str(n)):
print(k**2, end=', ')
break
n += 1 # Derek Orr, Jul 31 2014
(Python)
from gmpy2 import isqrt
def A018796(n):
if n == 0:
return 0
else:
d, nd = 1, n
while True:
x = (isqrt(nd-1)+1)**2
if x < nd+d:
return int(x)
d *= 10
nd *= 10 # Chai Wah Wu, May 23 2016
(PARI) \\Set precision high enough (for the cases where n+1 is a square)!
a(n) = {my(v=vector(2)); if(issquare(n), return(n), v=[sqrt(n), sqrt(n+1-(10^-((#digits(n)+7))))]; while(ceil(v[1])>floor(v[2]), v*=sqrt(10))); ceil(v[1])^2
} \\ David A. Corneth, May 22 2016
CROSSREFS
Sequence in context: A068165 A086935 A077689 * A029945 A264906 A263095
KEYWORD
nonn,base,easy
AUTHOR
EXTENSIONS
a(0)=0 prepended by Zak Seidov, May 22 2016
STATUS
approved

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Last modified March 19 07:18 EDT 2024. Contains 370954 sequences. (Running on oeis4.)