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Rémy Sigrist, <a href="/A333441/b333441.txt">Table of n, a(n) for n = 1..8789</a> (terms < 2^16)

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The term 0 is included by convention (we consider here that it has no digit).

Every term belong to A059012.

This sequence has connections with A014486; in both sequences digits are balanced in some way.

The first terms, alongside their binary representation with a possible pairing, are:

n a(n) bin(a(n))

-- ---- ------------

1 0 0

2 3 (11)

3 9 (1(00)1)

4 12 (11)(00)

5 15 (11)(11)

6 33 (1(00)(00)1)

7 36 (1(00)1)(00)

8 39 (1(00)1)(11)

9 45 (1(0(11)0)1)

10 48 (11)(00)(00)

11 51 (11)(00)(11)

12 54 (11)(0(11)0)

13 57 (11)(1(00)1)

14 60 (11)(11)(00)

15 63 (11)(11)(11)

Cf. A014486, A059012, A333440.

allocated for Rémy Sigrist

Numbers where each binary digit can be paired with a digit of the same value at another position so that two pairs can be nested but cannot otherwise overlap.

0, 3, 9, 12, 15, 33, 36, 39, 45, 48, 51, 54, 57, 60, 63, 129, 132, 135, 141, 144, 147, 150, 153, 156, 159, 165, 177, 180, 183, 189, 192, 195, 198, 201, 204, 207, 210, 216, 219, 222, 225, 228, 231, 237, 240, 243, 246, 249, 252, 255, 513, 516, 519, 525, 528, 531

1,2

This sequence is a binary variant of A333440.

(PARI) is(n, base=2) = { my (u=0, s=0); while (n, my (d=n%base); if (u && s%base==d, u--; s\=base, u++; s=s*base+d); n\=base); u==0 }

Cf. A333440.

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nonn,base

Rémy Sigrist, Mar 21 2020

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allocated for Rémy Sigrist

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