OFFSET
1,2
COMMENTS
The terms a(n) are unbounded. The smallest n with a(n) = m, n_min(m), however may be exorbitantly large, even for small m. It can be calculated by the following recurrence: n_min(1) = 1; n_min(2) = 2; n_min(m) = 2^n_min(m-1) - 1 {if m > 2};
LINKS
FORMULA
a(1) = 1; for n > 1, a(n) = 1 + a(A000120(n)), where A000120 gives the number of occurrences of digit 1 in binary representation of n.
a(n) = 1 + A180094(n). - Antti Karttunen, Jul 09 2017
EXAMPLE
a(13) = 4 because 13 = (1101) -> (1+1+0+1 = 11) -> (1+1 = 10) -> (1+0 = 1) = 1. (Three iterations were required to reach 1.)
MAPLE
for n from 1 to 500 do h := n:a[n] := 1:while(h>1) do a[n] := a[n]+1: b := convert(h, base, 2):h := sum(b[j], j=1..nops(b)):od:od:seq(a[j], j=1..500);
MATHEMATICA
Table[Length[NestWhileList[Total[IntegerDigits[#, 2]]&, n, #>1&]], {n, 110}] (* Harvey P. Dale, Oct 10 2011 *)
PROG
(PARI) A078627(n) = { my(k=1); while(n>1, n = hammingweight(n); k += 1); (k); }; \\ Antti Karttunen, Jul 09 2017
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Frank Schwellinger (nummer_eins(AT)web.de), Dec 12 2002
EXTENSIONS
Description corrected by Antti Karttunen, Jul 09 2017
STATUS
approved