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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, May 22 2016 (first 10000 terms from Chai Wah Wu) EXAMPLE Among 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 A263095 Adjacent sequences:  A018793 A018794 A018795 * A018797 A018798 A018799 KEYWORD nonn,base,easy AUTHOR EXTENSIONS a(0)=0  prepended by Zak Seidov, May 22 2016 STATUS approved

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Last modified January 16 14:59 EST 2022. Contains 350376 sequences. (Running on oeis4.)