A171797 A modified Sisyphus function: a(n) = concatenation of (number of digits in n) (number of even digits) (number of odd digits).

110, 101, 110, 101, 110, 101, 110, 101, 110, 101, 211, 202, 211, 202, 211, 202, 211, 202, 211, 202, 220, 211, 220, 211, 220, 211, 220, 211, 220, 211, 211, 202, 211, 202, 211, 202, 211, 202, 211, 202, 220, 211, 220, 211, 220, 211, 220, 211, 220, 211, 211, 202

Offset: 0

Author

N. J. A. Sloane, Oct 15 2010

Keywords

• nonn
• base
• easy
• look

Comments

Start with n, repeatedly apply the map i -> a(i). Then every number converges to 312. - Eric Angelini and Alexandre Wajnberg, Oct 15 2010

Examples

			11 has 2 digits, both odd, so a(11) = 202.
12 has 2 digits, one even and one odd, so a(12)=211. Then a(211) = 312.
		

References

• M. E. Coppenbarger, Iterations of a modified Sisyphus function, Fib. Q., 56 (No. 2, 2018), 130-141.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..25000

Crossrefs

Cf. A073053 (Sisyphus), A171798, A171813, A055642, A196563, A196564, A308002, A308003 (another version).

A100961 gives steps to reach 312.

Programs

Haskell

a171797 n = read $ concatMap (show . ($ n))
                   [a055642, a196563, a196564] :: Integer
-- Reinhard Zumkeller, Feb 22 2012, Oct 15 2010

Maple

nevenDgs := proc(n) local a, d; a := 0 ; for d in convert(n,base,10) do if type(d,'even') then a :=a +1 ; end if; end do; a ; end proc:
cat2 := proc(a,b) local ndigsb; ndigsb := max(ilog10(b)+1,1) ; a*10^ndigsb+b ; end:
catL := proc(L) local a, i; a := op(1,L) ; for i from 2 to nops(L) do a := cat2(a,op(i,L)) ; end do; a; end proc:
A055642 := proc(n) max(1,ilog10(n)+1) ; end proc:
A171797 := proc(n) local n1,n2 ; n1 := A055642(n) ; n2 := nevenDgs(n) ; catL([n1,n2,n1-n2]) ; end proc:
seq(A171797(n),n=1..80) ; # R. J. Mathar, Oct 15 2010 and Oct 18 2010

Python

def a(n):
    s = str(n); e = sum(d in "02468" for d in s)
    return int("".join(map(str, (len(s), e, len(s)-e))))
print([a(n) for n in range(52)]) # Michael S. Branicky, Jun 15 2021

Extensions

More terms from R. J. Mathar, Oct 15 2010

a(0) added by N. J. A. Sloane, May 12 2019