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User: Sean Lipton

Sean Lipton has authored 2 sequences.

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

Sean Lipton, Jul 14 2020

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.

			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

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

Cf. A308055, A309123.

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

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).

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.

Original entry on oeis.org

2, 5, 23, 48, 22, 15, 39, 63, 251, 501, 224, 474, 689, 2625, 5124, 22637, 47579, 68978, 83053, 28819, 53684, 2317, 4814, 6939, 26342, 51325, 71642, 84642, 290933, 1705676, 4129984, 20322363, 45080332, 67141889, 25911752, 16097128, 12687446, 35619442, 59682026

Offset: 1

Sean Lipton, May 09 2019

The sequence contains the following squares: 315844, 289, 81, 9, and is eventually periodic. - Rémy Sigrist, Jul 13 2019

			a(1) = 2;
25 is the smallest square with 2 as a prefix;
a(2) = sqrt(25) = 5;
529 is the smallest square with 5 as a prefix;
a(3) = sqrt(529) = 23;
2304 is the smallest square with 23 as a prefix;
a(4) = sqrt(2304) = 48; etc.

Rémy Sigrist, Table of n, a(n) for n = 1..100
Rémy Sigrist, PARI program for A308055

Cf. A000290 (squares), A018851.

PARI
```
\\ See Links section.
```

From Rémy Sigrist, Jul 13 2019: (Start)
a(n+1) = A018851(a(n)).
a(n + 4) = a(n) for n >= 83. (End)

a(31)-a(39) from Jon E. Schoenfield, May 10 2019

Comments corrected by Rémy Sigrist, Jul 13 2019

cp's OEIS Frontend

User: Sean Lipton

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

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