A304024 a(n) is the largest integer with n digits in base 3/2.

2, 22, 212, 2122, 21222, 212212, 2122112, 21221112, 212211122, 2122111222, 21221112212, 212211122122, 2122111221212, 21221112212112, 212211122121122, 2122111221211222, 21221112212112212, 212211122121122122

Offset

0,1

Comments

Every number starts and ends with 2 and contains only twos and ones.

Removing the last digit produces sequence A304272 of the largest even integers in base 3/2.

The value of this sequence in base 10 is A304025.

When adding 1 to the value of this sequence we get A070885.

The largest integer with a given number of digits in base 3/2 can be produced directly from the smallest number, sequence A304023, by replacing 21 at the beginning and 0 at the end with 2, and by shifting the rest up by 1, see sequence A304023.

Links

Table of n, a(n) for n=0..17.

Formula

a(1) = 2, for n > 1, a(n) = 10 * a(n - 1) + 2 if A304025(n - 1) is even. Otherwise, a(n) = 10 * a(n - 1) - 8. - David A. Corneth, May 11 2018

Example

The number 5 in base 3/2 is 22, and the number 6 is 210. Therefore, 22 is the largest two-digit integer.

Prog

(PARI) first(n) = {my(res=vector(n), c = 2); res[1]=2; for(i=2, n, res[i] = 10 * res[i-1] + 2; if(c % 2 == 1, res[i] -= 10); c = 3 * c / 2 + if(c%2==0, 2, 1/2)); res} \\ David A. Corneth, May 11 2018

Crossrefs

Cf. A005428, A024629, A070885, A073941, A081848, A246435, A303500, A304023, A304025, A304272.

Sequence in context: A359856 A366919 A308313 * A239688 A350965 A336894

Adjacent sequences: A304021 A304022 A304023 * A304025 A304026 A304027

Keyword

nonn,base,easy

Author

Tanya Khovanova and PRIMES STEP Senior group, May 04 2018

Status

approved