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A050605 Column/row 2 of A050602: a(n) = add3c(n,2). 5
0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 3, 3, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 4, 4, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 3, 3, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 5, 5, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 3, 3, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

It seems that (n - Sum_{k=1..n} a(k) )/log(n) is bounded. - Benoit Cloitre, Oct 03 2002

2^a(n) is the highest power of 2 dividing the n-th triangular number n*(n+1)/2. - Benoit Cloitre, Oct 03 2002

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..5000

MAPLE

nmax:=80; with(Bits): add3c := proc(a, b) option remember; if(0 = And(a, b)) then RETURN(0); else RETURN(1+add3c(Xor(a, b), 2*And(a, b))); fi; end: for n from 0 to nmax do a(n):=add3c(n, 2) od: seq(a(n), n=0..nmax); # Johannes W. Meijer, Jun 18 2009

MATHEMATICA

Table[IntegerExponent[(n + 1)(n + 2)/2, 2], {n, 0, 100}] (* Jean-Fran├žois Alcover, Mar 04 2016 *)

PROG

(PARI) a(n)=valuation(n*(n+1)/2, 2)

(MAGMA) [Valuation(n*(n+1)/2, 2): n in [1..120]]; // Vincenzo Librandi, Aug 11 2017

CROSSREFS

Bisection gives column/row 1 of A050602: A007814.

From Johannes W. Meijer, Jun 18 2009: (Start)

a(4*n+2) = A001511(n).

Cf. A161737 and A069834.

(End)

Sequence in context: A295520 A295335 A227838 * A060571 A131555 A293209

Adjacent sequences:  A050602 A050603 A050604 * A050606 A050607 A050608

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 22 1999

STATUS

approved

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Last modified February 18 02:09 EST 2018. Contains 299297 sequences. (Running on oeis4.)