A018796 Smallest square that begins with n.

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

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

Cf. A018851, A077502.

Sequence in context: A068165 A086935 A077689 * A029945 A264906 A374935

Adjacent sequences: A018793 A018794 A018795 * A018797 A018798 A018799

Keyword

nonn,base,easy

Author

David W. Wilson

Extensions

a(0)=0 prepended by Zak Seidov, May 22 2016

Status

approved