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A103529 Values of A102370 which are >= a new power of 2. 4
0, 3, 6, 15, 28, 61, 126, 251, 504, 1017, 2042, 4095, 8180, 16373, 32758, 65523, 131056, 262129, 524274, 1048567, 2097148, 4194285, 8388590, 16777195, 33554408, 67108841, 134217706, 268435439, 536870884, 1073741797, 2147483622 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

David Applegate and N. J. A. Sloane, Table of n, a(n) for n = 1..62

David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].

David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

FORMULA

a(n) = 2^(n-1) - (n-1) + Sum_{ k >= 1, k == n-1 mod 2^k } 2^k.

a(n+1) = 2^n + A102371(n) for n>=1. a(n) = 2^n - A103530(n). - Philippe Deléham, Mar 30 2005

a(0)=0, a(1)=3, for n>1, a(n)= a(n-1) XOR (a(n-1)+n), where XOR is the bitwise exclusive-or operator. - Alex Ratushnyak, Apr 21 2012

EXAMPLE

The initial values of A102370 are 0*, 3*, 6*, 5, 4, 15*, 10, 9, 8, 11, 14, 13, 28*, 23, ... and the starred terms are those which exceed the next power of 2. Their indices (except for the zero term) are given by A000325.

PROG

(Python)

a=3

print 0,

for i in range(2, 55):

. print a,

. a ^= a+i

# Alex Ratushnyak, Apr 21 2012

CROSSREFS

Cf. A102370, A103530.

Sequence in context: A300761 A069712 A076971 * A185378 A285563 A285543

Adjacent sequences:  A103526 A103527 A103528 * A103530 A103531 A103532

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane and David Applegate, Mar 22 2005

STATUS

approved

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Last modified August 5 21:50 EDT 2020. Contains 336213 sequences. (Running on oeis4.)