A059307 Numbers n such that base 10 representation of n does not contain a block of digits which is a square: blocks like 0, 1, 4, 9, 36, 121, ... are forbidden.

2, 3, 5, 6, 7, 8, 22, 23, 26, 27, 28, 32, 33, 35, 37, 38, 52, 53, 55, 56, 57, 58, 62, 63, 65, 66, 67, 68, 72, 73, 75, 76, 77, 78, 82, 83, 85, 86, 87, 88, 222, 223, 226, 227, 228, 232, 233, 235, 237, 238, 262, 263, 265, 266, 267, 268, 272, 273, 275, 276, 277, 278, 282

Offset

1,1

Comments

"Squarefree" integers. The usual definition of "squarefree" means that there is no square as divisor, but here we consider numbers without any square in their decimal expansion. Of the first 1000 integers only 232 are in the sequence, while 608 are squarefree in the usual sense. - Zak Seidov, Sep 26 2002

Sequence is infinite, since numbers consisting of only the digits 2, 3, 7, and 8 cannot contain squares. In particular this shows a(n) << n^1.661. - Charles R Greathouse IV, Mar 05 2014

Links

Table of n, a(n) for n=1..63.

Example

a(7) = 22 because both 2 and 22 are nonsquares.
323 and 326 are members because they have no squares 0, 1, 4, 9, 16, 25, 36... in their decimal expansion; while the two numbers between, 324 and 325, are not members because 324 contains square 4 and 325 - square 25.

Crossrefs

A subsequence of A000037.

Sequence in context: A050025 A255430 A074492 * A357961 A159635 A068938

Adjacent sequences: A059304 A059305 A059306 * A059308 A059309 A059310

Keyword

nonn,base

Author

Noam Katz (noamkj(AT)hotmail.com), Jan 25 2001

Status

approved