OFFSET
0,1
COMMENTS
If we start with n and repeatedly apply the map i -> a(i), it appears that we eventually reach one of the two fixed points 22 or 231, or enter the two-cycle (33, 220). Are there any other possibilities? This is in contrast to the behavior of the closely related A308003.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
M. E. Coppenbarger, Iterations of a modified Sisyphus function, Fib. Q., 56 (No. 2, 2018), 130-141.
EXAMPLE
11 has 2 digits, both odd, so a(11)=220.
12 has 2 digits, one even and one odd, so a(12)=121. Then a(121) = 231, a fixed point.
22 has two digits, both even, so 22 -> 22, another fixed point (leading zeros are omitted).
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:
A308005 := proc(n) local n1, n2 ; n1 := A055642(n) ; n2 := nevenDgs(n) ; catL([n1-n2, n1, n2]) ; end proc:
[seq(A308005(n), n=0..80)];
MATHEMATICA
A308005[n_] := FromDigits[Flatten[IntegerDigits[{Count[#, _?OddQ], Length[#], Count[#, _?EvenQ]}]]] & [IntegerDigits[n]];
Array[A308005, 100, 0] (* Paolo Xausa, Jan 20 2026 *)
PROG
(Python)
def a(n): # OTE
s = str(n)
e = sum(1 for c in s if c in "02468")
return int(str(len(s)-e) + str(len(s)) + str(e))
print([a(n) for n in range(65)]) # Michael S. Branicky, Jan 13 2026
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, May 12 2019
STATUS
approved