OFFSET
1,1
COMMENTS
Obviously f(k) < k for k more than 3000. The Mathematica program below calculates f applied hundred times for every number up to 3000. After that the manual checking shows that the output is the exact list. There are three cycles. First: 70, 129, 518, 290, 517, 162. Second: 5, 32, 12, 6, 64, 80, 257, 164, 82, 260, 69, 576, 224, 24, 20. Third: 98, 768, 448, 288, 516.
EXAMPLE
f(70) = 2^7 + 2^0 = 129, f(129) = 2^1 + 2^2 + 2^9 = 518, f(518) = 2^5 + 2^1 + 2^8 = 290, f(290) = 2^2 + 2^9 + 2^0 = 517, f(517) = 2^5 + 2^1 + 2^7 = 162, f(162) = 2^1 + 2^6 + 2^2 = 70. That means that all the numbers 70, 129, 518, 290, 517, 162 belong to this sequence.
MATHEMATICA
s2p[n_] := Plus @@ (2^IntegerDigits[n]); Union[Table[Nest[s2p, n, 100], {n, 3000}]]
CROSSREFS
KEYWORD
base,fini,full,nonn
AUTHOR
Tanya Khovanova, Jan 05 2007
STATUS
approved