A030666 Smallest nontrivial extension of n which is a square.
16, 25, 36, 49, 529, 64, 729, 81, 900, 100, 1156, 121, 1369, 144, 1521, 169, 1764, 1849, 196, 2025, 2116, 225, 2304, 2401, 256, 2601, 2704, 289, 2916, 3025, 3136, 324, 3364, 3481, 35344, 361, 3721, 3844, 3969, 400, 41209, 4225, 4356, 441
Offset: 1
Examples
80 is not a perfect square, but 81 = 9^2, so a(8) = 81. Although 9 is already a square, we need to append at least one digit. However, none of 90, 91, 92, ..., 99 are squares. Then we try 900 = 30^2, so a(9) = 900.
Links
- N. J. A. Sloane, Table of n, a(n) for n = 1..20000
Programs
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Maple
# Program which computes 20000 terms, from N. J. A. Sloane, Nov 24 2015 for b from 1 to 20000 do sw1:=-1: for p from 1 to 6 do bp:=b*10^p; for i from 0 to 10^p-1 do if issqr(bp+i) then lprint(b,bp+i); sw1:=1; break; fi; od: if sw1 > 0 then break; fi; od: if sw1 < 0 then lprint("failed at b = ",b); fi; od:
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Python
from gmpy2 import isqrt def A030666(n): d, nd = 10, 10*n while True: x = (isqrt(nd-1)+1)**2 if x < nd+d: return int(x) d *= 10 nd *= 10 # Chai Wah Wu, May 24 2016
Formula
a(n) = A030667(n)^2.
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