A026354 a(n) = a(m) if a(m) has already occurred exactly once and n = a(m)+m-2, else a(n) = least positive integer that has not yet occurred.

1, 2, 3, 3, 4, 5, 4, 6, 5, 7, 8, 6, 9, 10, 7, 11, 8, 12, 13, 9, 14, 10, 15, 16, 11, 17, 18, 12, 19, 13, 20, 21, 14, 22, 23, 15, 24, 16, 25, 26, 17, 27, 18, 28, 29, 19, 30, 31, 20, 32, 21, 33, 34, 22, 35, 23, 36, 37, 24, 38, 39, 25, 40, 26, 41, 42

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Jeffrey Shallit, Automaton for a(n)

Crossrefs

Cf. A026272.

Programs

PARI

A026354=vector(2+#A026242,n,if(n>3,A026242[n-2]+2,n)) \\ Assumes the vector A026242 is defined, see there for PARI code. - M. F. Hasler, Sep 17 2014

Formula

a(n)=n for n<4, a(n)=A026242(n-2)+2 for all n>2, a(n)=A026272(n-4)+3 for n>4. - M. F. Hasler, Sep 17 2014

There is a 35-state automaton that accepts, in parallel, the Fibonacci (Zeckendorf) representation of n and a(n). See the file a026354.pdf. - Jeffrey Shallit, Dec 21 2023