A103529 Values of A102370 which are >= a new power of 2.

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

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, end=', ')
for i in range(2, 55):
    print(a, end= ', ')
    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