

A053738


If n is in sequence then 2n and 2n+1 are not (and 1 is in the sequence); numbers with an odd number of digits in binary.


5



1, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109
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OFFSET

1,2


COMMENTS

Runs of successive numbers have lengths which are powers of 4.
Apparently, for any m>=1, 2^m is the largest power of 2 dividing sum(k=1,n,binomial(2k,k)^m) if and only if n is in the sequence.  Benoit Cloitre, Apr 27 2003
Numbers that begin with a 1 in base 4.  Michel Marcus, Dec 05 2013


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
M. Madritsch, S. Wagner, A central limit theorem for integer partitions, Monatsh. Math. 161 (1) (2010) 85114 doi:10.1007/s006050090126y. Section 4.3.


FORMULA

G.f.: x/(1x)^2 + Sum_{k>=1} 2^(2k1)*x^((4^k+2)/3)/(1x).  Robert Israel, Dec 28 2016


MAPLE

seq(seq(i, i=4^k..2*4^k1), k=0..5); # Robert Israel, Dec 28 2016


MATHEMATICA

Select[Range[110], OddQ[IntegerLength[#, 2]]&] (* Harvey P. Dale, Sep 29 2012 *)


PROG

(PARI) isok(n, b=4) = digits(n, b)[1] == 1; \\ Michel Marcus, Dec 05 2013


CROSSREFS

Cf. A029837, A079112.
Sequence in context: A037355 A294228 A046300 * A327101 A327082 A154787
Adjacent sequences: A053735 A053736 A053737 * A053739 A053740 A053741


KEYWORD

base,easy,nonn


AUTHOR

Henry Bottomley, Apr 06 2000


STATUS

approved



