STATUS
reviewed
approved
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Revision History for A078627
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Write n in binary; repeatedly sum the "digits" until reaching 1; a(n) = 1 + number of steps required.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
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).)
STATUS
proposed
editing
STATUS
editing
proposed
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).
EXTENSIONS
Description corrected by Antti Karttunen, Jul 09 2017
NAME
Write n in binary; repeatedly sum the "digits" until reaching 1; a(n) = 1 + number of steps required.
LINKS
<a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
FORMULA
m a(1) = 1; for n > 1, a(n) = "1 + a(A000120(n)), where A000120 gives the number of occurrences of binary digit 1 in n"; a(n) = 1 (if n = 1); a(binary representation of n) = 1 + a(m) otherwise.
a(n) = 1 + A180094(n). - Antti Karttunen, Jul 09 2017
CROSSREFS
One more than A180094.
LINKS
Antti Karttunen, <a href="/A078627/b078627.txt">Table of n, a(n) for n = 1..8192</a>
PROG
(PARI) A078627(n) = { my(k=1); while(n>1, n = hammingweight(n); k += 1); (k); }; \\ Antti Karttunen, Jul 09 2017
CROSSREFS
Cf. A000120.
STATUS
approved
editing
MATHEMATICA
Table[Length[NestWhileList[Total[IntegerDigits[#, 2]]&, n, #>1&]], {n, 110}] (* From _Harvey P. Dale, _, Oct 10 2011 *)
STATUS
editing
approved