A336251 a(1) = 15; for n > 1, a(n)^2 is the smallest square that begins with a(n-1) in base 6.

15, 57, 111, 155, 183, 199, 508, 812, 171, 471, 319, 643, 913, 1088, 2909, 11650, 9518, 21074, 31357, 93691, 396693, 55540, 50905, 119374, 182804, 226216, 251647, 265415, 111280, 72055, 142024, 13567, 25160, 34262, 39982, 105795, 172093, 537634

Offset

1,1

Comments

The sequence becomes periodic after 491 terms with a period of 10.

The only square in this sequence is 25 and the sequence becomes periodic two terms later.

The maximum value is a(226) = 325880259349618.

Links

Sean Lipton, Table of n, a(n) for n = 1..600

Formula

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.

For n > 481, a(n) = a(n+10).

Example

The first 10 a(n) alongside the base 6 representations of a(n) and squares of a(n+1):
  n   a(n)  a(n) b6  a(n+1)^2 b6
  --  ----  -------  -----------
   1    15       23        23013
   2    57      133       133013
   3   111      303       303121
   4   155      415       415013
   5   183      503       503201
   6   199      531      5310424
   7   508     2204     22044304
   8   812     3432       343213
   9   171      443      4431013
  10   471     2103      2103041

Prog

(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

Crossrefs

Cf. A308055, A309123.

Sequence in context: A140379 A020222 A256867 * A158482 A184223 A084815

Adjacent sequences: A336248 A336249 A336250 * A336252 A336253 A336254

Keyword

nonn,base

Author

Sean Lipton, Jul 14 2020

Status

approved