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A078627 Write n in binary; repeatedly sum the "digits" until reaching 1; a(n) = 1 + number of steps required. 3
1, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 3, 2, 3, 3, 4, 3, 4, 4, 3, 3, 4, 4, 3, 4, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 3, 3, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4, 3, 4, 3, 3, 4, 4, 3, 3, 4, 3, 4, 4, 4, 2, 3, 3, 4, 3, 4, 4, 3, 3, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4, 3, 4, 3, 3, 4, 4, 3, 3, 4, 3, 4, 4, 4, 3, 4, 4, 3, 4, 3, 3, 4, 4, 3 (list; graph; refs; listen; history; text; internal format)
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

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences related to binary expansion of n

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

Cf. A000120.

One more than A180094.

Sequence in context: A129759 A137467 A261461 * A106370 A128630 A273040

Adjacent sequences:  A078624 A078625 A078626 * A078628 A078629 A078630

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

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Last modified August 8 09:16 EDT 2020. Contains 336293 sequences. (Running on oeis4.)