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A030666 Smallest nontrivial extension of n which is a square. 5

%I #22 Apr 25 2020 02:01:47

%S 16,25,36,49,529,64,729,81,900,100,1156,121,1369,144,1521,169,1764,

%T 1849,196,2025,2116,225,2304,2401,256,2601,2704,289,2916,3025,3136,

%U 324,3364,3481,35344,361,3721,3844,3969,400,41209,4225,4356,441

%N Smallest nontrivial extension of n which is a square.

%C A trivial extension would mean appending no digits at all when n is already a square. With trivial extensions allowed, this sequence becomes A018796.

%H N. J. A. Sloane, <a href="/A030666/b030666.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = A030667(n)^2.

%e 80 is not a perfect square, but 81 = 9^2, so a(8) = 81.

%e 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.

%p # Program which computes 20000 terms, from _N. J. A. Sloane_, Nov 24 2015

%p for b from 1 to 20000 do

%p sw1:=-1:

%p for p from 1 to 6 do

%p bp:=b*10^p;

%p for i from 0 to 10^p-1 do

%p if issqr(bp+i) then lprint(b,bp+i); sw1:=1; break; fi;

%p od:

%p if sw1 > 0 then break; fi;

%p od:

%p if sw1 < 0 then lprint("failed at b = ",b); fi;

%p od:

%o (Python)

%o from gmpy2 import isqrt

%o def A030666(n):

%o d, nd = 10, 10*n

%o while True:

%o x = (isqrt(nd-1)+1)**2

%o if x < nd+d:

%o return int(x)

%o d *= 10

%o nd *= 10 # _Chai Wah Wu_, May 24 2016

%Y Cf. A030667, A030686, A018796.

%Y See A264604 for another version (first differs at a(9)).

%K nonn,base

%O 1,1

%A _Patrick De Geest_

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)