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

0,1

Comments

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

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

Example

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.

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) ;

Prog

(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

Crossrefs

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

A073054 gives steps to reach 132.

Sequence in context: A266301 A163597 A266606 * A288057 A288128 A281849

Adjacent sequences: A308000 A308001 A308002 * A308004 A308005 A308006

Keyword

nonn,base,easy

Author

N. J. A. Sloane, May 12 2019

Status

approved