A260112 Minimal number of steps to get from 0 to n by (a) adding 1 or (b) multiplying by 4.

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

Offset

0,3

Comments

a(n) = (Weight of quaternary expansion of n) + (length of quaternary expansion of n) - 1.

Links

Peter Kagey, Table of n, a(n) for n = 0..10000

Formula

a(n) = A053737(n) + A110591(n) - 1. - Michel Marcus, Jul 17 2015

Example

For a(308) = 9, the nine steps are: 308 => 77 => 76 => 19 => 18 => 17 => 16 => 4 => 1 => 0.

Maple

a:= n-> (l-> nops(l)+add(i, i=l)-1)(convert(n, base, 4)):
seq(a(n), n=0..105);  # Alois P. Heinz, Jul 16 2015

Prog

(Ruby) def a(n); n.to_s(4).length + n.to_s(4).split('').map(&:to_i).reduce(:+) - 1 end
(PARI) a(n)=sumdigits(n, 4)+#digits(n, 4)-1 \\ Charles R Greathouse IV, Jul 16 2015
(Haskell)
c i = if i `mod` 4 == 0 then i `div` 4 else i - 1
b 0 foldCount = foldCount
b sheetCount foldCount = b (c sheetCount) (foldCount + 1)
a260112 n = b n 0 -- Peter Kagey, Sep 02 2015

Crossrefs

Analogous sequences with a different multiplier k: A056792 (k=2), A061282 (k=3).

Cf. A053737, A110591, A007090: base 4 sequences.

Sequence in context: A286534 A324532 A324390 * A361838 A213183 A125929

Adjacent sequences: A260109 A260110 A260111 * A260113 A260114 A260115

Keyword

nonn,easy

Author

Peter Kagey, Jul 16 2015

Status

approved