A137416 a(n) = smallest nontrivial square (i.e., not a multiple of 10) with exactly n identical adjacent digits.

1, 144, 1444, 1666681, 111112681, 3333330225, 132922222225, 1433333333961, 2582708888888881, 28777777777780164, 88888888888905609, 55555555555566005625, 2222222222222640225, 4777777777777776827176356, 20193204988888888888888804, 174881683455555555555555556, 175246811111111111111111080489, 9935069953444444444444444444176

Offset

1,2

Comments

Since a(13) < a(12), a(13) is actually the smallest nontrivial square with at least 12 identical adjacent digits (cf. A169859), while a(12) is the smallest containing 12, but not more than 12, identical adjacent digits. - Jon E. Schoenfield, May 16 2010

a(n) >= A169859(n) with equality taking place when A169859(n) contains exactly n identical adjacent digits. - Max Alekseyev, Dec 29 2024

Links

Table of n, a(n) for n=1..18.

Example

a(3) = 1444 because it has 3 adjacent 4's, and no square less than 1444 has 3 adjacent digits which are the same.

Crossrefs

Cf. A169859.

Sequence in context: A023096 A223435 A169859 * A109117 A209205 A223594

Adjacent sequences: A137413 A137414 A137415 * A137417 A137418 A137419

Keyword

nonn,base

Author

Randy L. Ekl, Apr 15 2008

Extensions

a(11) from Donovan Johnson, May 08 2010

a(12)-a(14) from Jon E. Schoenfield, May 16 2010

a(15)-a(18) from Max Alekseyev, Dec 29 2024

Status

approved