

A049502


Major index of n, 2nd definition.


10



0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 0, 1, 0, 0, 0, 1, 2, 2, 3, 4, 3, 3, 0, 1, 2, 2, 0, 1, 0, 0, 0, 1, 2, 2, 3, 4, 3, 3, 4, 5, 6, 6, 4, 5, 4, 4, 0, 1, 2, 2, 3, 4, 3, 3, 0, 1, 2, 2, 0, 1, 0, 0, 0, 1, 2, 2, 3, 4, 3, 3, 4, 5, 6, 6, 4, 5, 4, 4, 5, 6, 7, 7, 8, 9, 8, 8, 5, 6, 7, 7, 5, 6, 5, 5, 0, 1, 2, 2, 3, 4, 3, 3, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,11


COMMENTS

a(A023758(n)) = 0; a(A101082(n)) > 0.  Reinhard Zumkeller, Jun 17 2015


REFERENCES

D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; cf. p. 89.


LINKS

Lars Blomberg, Table of n, a(n) for n = 0..10000


FORMULA

Write n in binary; add positions where there are 1's followed by 0's, counting from right.


EXAMPLE

83 = 1010011 has 1's followed by 0's in positions 2 and 5 (reading from the right), so a(83)=7.


MAPLE

A049502 := proc(n)
local a, ndgs, p ;
a := 0 ;
ndgs := convert(n, base, 2) ;
for p from 1 to nops(ndgs)1 do
if op(p, ndgs) op(p+1, ndgs) = 1 then
a := a+p ;
end if;
end do:
a ;
end proc: # R. J. Mathar, Oct 17 2012


MATHEMATICA

Table[Total[Flatten[Position[Partition[Reverse[IntegerDigits[n, 2]], 2, 1], _?(#=={1, 0}&)]]], {n, 0, 110}] (* Harvey P. Dale, Oct 05 2013 *)


PROG

(Haskell)
a049502 = f 0 1 where
f m i x = if x <= 4
then m else f (if mod x 4 == 1
then m + i else m) (i + 1) $ div x 2
 Reinhard Zumkeller, Jun 17 2015
(Python)
def m(n):
x=bin(int(n))[2:][::1]
s=0
for i in range(1, len(x)):
if x[i1]=="1" and x[i]=="0":
s+=i
return s
for i in range(0, 10001):
print str(i)+" "+str(m(i)) \\ Indranil Ghosh, Dec 22 2016


CROSSREFS

Cf. A049501, A037800.
Cf. A023758, A101082.
Sequence in context: A004586 A116511 A248211 * A242284 A306595 A292592
Adjacent sequences: A049499 A049500 A049501 * A049503 A049504 A049505


KEYWORD

nonn,base,nice,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Erich Friedman, Feb 19 2000


STATUS

approved



