OFFSET
0,2
COMMENTS
Numbers m such that a(2^m*(2^(m + 1) - 1) + 1) = 2^m are 0, 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 15, 18, 20, 21, ...
Numbers t such that a(t) = 2 are 7, 8, 10, 33, 35, 36, 39, 40, 42, 47, 48, 50, ...
Numbers t such that a(t) > t are 0, 1, 3, 5, 9, 11, 13, 15, 17, 18, 19, 20, 21, ...
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..8192
Altug Alkan, Line graph of a(n+1)-a(n) for n <= 2^13
Altug Alkan, A logarithmic scatterplot of a(n)
FORMULA
a(n) <> n for all n >= 0.
a(n) <= 5*n for all n >= 1.
a(2^m - 1) = 1 for all m >= 1.
a(2^m - 2^2) = 2^2 - 1 for all m >= 3.
a(2^m - 2^3) = 2^3 - 1 for all m >= 5.
a(2^m - 2^4) = 2^4 - 1 for all m >= 7.
a(2^m - 2^5) = 2^5 - 1 for all m >= 10.
a(2^m - 2^6) = 2^6 - 1 for all m >= 13.
a(2^m - 2^7) = 2^7 - 1 for all m >= 17.
a(2^m - 2^8) = 2^8 - 1 for all m >= 21.
a(2^m - 2^9) = 2^9 - 1 for all m >= 26.
a(2^(p - 1)) = 2^(p - 1) - 1 and a(2^(p - 1) - 1) = 2^p + 1 for all primes p.
a(2^(p - 1) + 1) = 2^p + 3 for all primes p >= 5.
EXAMPLE
PROG
(PARI) a(n) = {my(k=1); while (hammingweight(k+n)/#binary(k+n) != hammingweight(k) /#binary(k), k++); k; }
CROSSREFS
KEYWORD
AUTHOR
Altug Alkan, Oct 05 2017
STATUS
approved