A308003 A modified Sisyphus function: a(n) = concatenation of (number of even digits in n) (number of digits in n) (number of odd digits in n).

110, 11, 110, 11, 110, 11, 110, 11, 110, 11, 121, 22, 121, 22, 121, 22, 121, 22, 121, 22, 220, 121, 220, 121, 220, 121, 220, 121, 220, 121, 121, 22, 121, 22, 121, 22, 121, 22, 121, 22, 220, 121, 220, 121, 220, 121, 220, 121, 220, 121, 121, 22, 121, 22, 121

Offset: 0

Author

N. J. A. Sloane, May 12 2019

Keywords

• nonn
• base
• easy

Comments

If we start with n and repeatedly apply the map i -> a(i), we eventually reach 132 (see A073054).

Examples

			11 has 2 digits, both odd, so a(11)=22 (leading zeros are omitted).
12 has 2 digits, one even and one odd, so a(12)=121. Then a(121) = 132.
		

References

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

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..28000

Crossrefs

Cf. A073053 (Sisyphus), A171797, A171798, A171813, A055642, A196563, A196564, A308002.

A073054 gives steps to reach 132.

Programs

Maple

# Maple code based on R. J. Mathar's code for A171797:
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:
A308003 := proc(n) local n1,n2 ; n1 := A055642(n) ; n2 := nevenDgs(n) ; catL([n2,n1,n1-n2]) ; end proc:
seq(A308003(n),n=0..80) ;

Python

def a(n):
    s = str(n)
    e = sum(1 for c in s if c in "02468")
    return int(str(e) + str(len(s)) + str(len(s)-e))
print([a(n) for n in range(55)]) # Michael S. Branicky, Mar 29 2022