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%I #27 Jul 22 2020 20:09:21
%S 15,57,111,155,183,199,508,812,171,471,319,643,913,1088,2909,11650,
%T 9518,21074,31357,93691,396693,55540,50905,119374,182804,226216,
%U 251647,265415,111280,72055,142024,13567,25160,34262,39982,105795,172093,537634
%N a(1) = 15; for n > 1, a(n)^2 is the smallest square that begins with a(n-1) in base 6.
%C The sequence becomes periodic after 491 terms with a period of 10.
%C The only square in this sequence is 25 and the sequence becomes periodic two terms later.
%C The maximum value is a(226) = 325880259349618.
%H Sean Lipton, <a href="/A336251/b336251.txt">Table of n, a(n) for n = 1..600</a>
%F a(n+1) = ceiling(sqrt(a(n)*6^i)) such that floor(sqrt((a(n)+1)*6^i-1)) > floor(sqrt(a(n)*6^i-1)) where i is a whole number and minimized.
%F For n > 481, a(n) = a(n+10).
%e The first 10 a(n) alongside the base 6 representations of a(n) and squares of a(n+1):
%e n a(n) a(n) b6 a(n+1)^2 b6
%e -- ---- ------- -----------
%e 1 15 23 23013
%e 2 57 133 133013
%e 3 111 303 303121
%e 4 155 415 415013
%e 5 183 503 503201
%e 6 199 531 5310424
%e 7 508 2204 22044304
%e 8 812 3432 343213
%e 9 171 443 4431013
%e 10 471 2103 2103041
%o (PARI) lista(nn) = {my(a = 15); for (n=2, nn, print1(a, ", "); my(i=1); while((sqrtint((a+1)*6^i-1) <= sqrtint(a*6^i-1)), i++); a = ceil(sqrt(a*6^i)););} \\ _Michel Marcus_, Jul 15 2020
%Y Cf. A308055, A309123.
%K nonn,base
%O 1,1
%A _Sean Lipton_, Jul 14 2020
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