A276692 Binary representations of n and n^2 have no common 3-digit substring.

0, 1, 2, 3, 5, 6, 7, 11, 23, 46, 85, 341, 1471, 2942, 5461, 21845, 349525, 1398101, 6025215, 12050430, 22369621, 89478485, 1431655765, 5726623061, 91625968981, 366503875925, 5864062014805, 23456248059221, 101086333501439, 202172667002878, 375299968947541, 1501199875790165

Offset

1,3

Comments

n such that A177062(n) <= 2.

Contains (4^m-1)/3 for m not divisible by 3.

Contains 2^(3*2^(k-1)-1) - 1 - Sum_{j=1..k-1} 2^(3*(2^(k-1)-2^(j-1))) and 2^(3*2^(k-1)) - 2 - Sum_{j=1..k-1} 2^(3*(2^(k-1)-2^(j-1))+1) for all k>=1.

Are there any other terms besides these and 0, 2, 7, 11?

Links

Table of n, a(n) for n=1..32.

Example

The binary representations of 11 and 11^2 are 1011 and 1111001.  The 3-digit substrings 101 and 011 of 1011 are not substrings of 1111001, so 11 is in the sequence.

Maple

f:= n -> length(StringTools:-LongestCommonSubString(convert(convert(n, binary), string), convert(convert(n^2, binary), string))):
select(f <= 2, [$0..1000]);

Crossrefs

Cf. A177062.

Sequence in context: A071251 A077571 A101730 * A169829 A189208 A270974

Adjacent sequences: A276689 A276690 A276691 * A276693 A276694 A276695

Keyword

nonn,base

Author

Robert Israel, Sep 13 2016

Extensions

a(27)-a(32) from Giovanni Resta, Aug 31 2019

Status

approved