A061282 Minimal number of steps to get from 0 to n by (a) adding 1 or (b) multiplying by 3. A stopping problem: begin with n and at each stage if a multiple of 3 divide by 3, otherwise subtract 1.

0, 1, 2, 2, 3, 4, 3, 4, 5, 3, 4, 5, 4, 5, 6, 5, 6, 7, 4, 5, 6, 5, 6, 7, 6, 7, 8, 4, 5, 6, 5, 6, 7, 6, 7, 8, 5, 6, 7, 6, 7, 8, 7, 8, 9, 6, 7, 8, 7, 8, 9, 8, 9, 10, 5, 6, 7, 6, 7, 8, 7, 8, 9, 6, 7, 8, 7, 8, 9, 8, 9, 10, 7, 8, 9, 8, 9, 10, 9, 10, 11, 5, 6, 7, 6, 7, 8, 7, 8, 9, 6, 7, 8, 7, 8, 9, 8, 9, 10, 7, 8

Offset: 0

Author

Henry Bottomley, Jun 06 2001

Keywords

• nonn
• easy

Comments

n > 0 occurs A001590(n+2) times in this sequence. - Peter Kagey, Jul 19 2015

a(n) gives the number of iterations of A260316 to reach 0. - Peter Kagey, Jul 22 2015

Examples

			a(25)=7 since 25=((0+1+1)*3+1+1)*3+1.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index to sequences related to the complexity of n

Crossrefs

Cf. A001590, A007089, A053735, A056792, A062153, A260316.

Analogous sequences with a different multiplier k: A056792 (k=2), A260112 (k=4).

Programs

Haskell

c i = if i `mod` 3 == 0 then i `div` 3 else i - 1
b 0 foldCount = foldCount
b sheetCount foldCount = b (c sheetCount) (foldCount + 1)
a061282 n = b n 0 -- Peter Kagey, Sep 02 2015

Maple

a:= n-> (l-> nops(l)+add(i, i=l)-1)(convert(n, base, 3)):
seq(a(n), n=0..105);  # Alois P. Heinz, Jul 16 2015

PARI

a(n)=sumdigits(n,3)+#digits(n,3)-1 \\ Charles R Greathouse IV, Jul 16 2015

Formula

a(n) = A062153(n) + A053735(n) = (number of base 3 digits of n) + (sum of base 3 digits of n)-1. a(3n) = a(n)+1, a(3n+1) = a(n)+2, a(3n+2) = a(n)+3; a(0)=0, a(1)=1, a(2)=2.