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A308055 a(1)=2; for n > 1, a(n) is the square root of the smallest square with a(n-1) as a prefix in base 10.

%I A308055 #18 Aug 14 2025 04:25:10
%S A308055 2,5,23,48,22,15,39,63,251,501,224,474,689,2625,5124,22637,47579,
%T A308055 68978,83053,28819,53684,2317,4814,6939,26342,51325,71642,84642,
%U A308055 290933,1705676,4129984,20322363,45080332,67141889,25911752,16097128,12687446,35619442,59682026
%N A308055 a(1)=2; for n > 1, a(n) is the square root of the smallest square with a(n-1) as a prefix in base 10.
%C A308055 The sequence contains the following squares: 315844, 289, 81, 9, and is eventually periodic. - _Rémy Sigrist_, Jul 13 2019
%H A308055 Rémy Sigrist, <a href="/A308055/b308055.txt">Table of n, a(n) for n = 1..100</a>
%H A308055 Rémy Sigrist, <a href="/A308055/a308055.gp.txt">PARI program for A308055</a>
%F A308055 From _Rémy Sigrist_, Jul 13 2019: (Start)
%F A308055 a(n+1) = A018851(a(n)).
%F A308055 a(n + 4) = a(n) for n >= 83. (End)
%e A308055 a(1) = 2;
%e A308055 25 is the smallest square with 2 as a prefix;
%e A308055 a(2) = sqrt(25) = 5;
%e A308055 529 is the smallest square with 5 as a prefix;
%e A308055 a(3) = sqrt(529) = 23;
%e A308055 2304 is the smallest square with 23 as a prefix;
%e A308055 a(4) = sqrt(2304) = 48; etc.
%o A308055 (PARI) \\ See Links section.
%Y A308055 Cf. A000290 (squares), A018851.
%K A308055 nonn,base,easy,look
%O A308055 1,1
%A A308055 _Sean Lipton_, May 09 2019
%E A308055 a(31)-a(39) from _Jon E. Schoenfield_, May 10 2019
%E A308055 Comments corrected by _Rémy Sigrist_, Jul 13 2019