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A175343
a(1)=1. a(n) = the smallest positive integer not yet occurring in the sequence such that (binary a(n)) OR (binary a(n-1)) is 2^k -1 for some k >=1.
3
1, 2, 3, 4, 7, 5, 6, 9, 14, 11, 12, 15, 8, 23, 10, 13, 18, 29, 19, 28, 27, 20, 31, 16, 47, 17, 30, 21, 26, 37, 58, 39, 24, 55, 25, 22, 41, 54, 43, 52, 59, 36, 63, 32, 95, 33, 62, 35, 60, 51, 44, 83, 45, 50, 61, 34, 93, 38, 57, 46, 49, 78, 53, 42, 85, 106, 87, 40, 119, 56, 71
OFFSET
1,2
COMMENTS
By "(binary a(n)) OR (binary a(n-1))", it is meant: Write a(n) and a(n-1) in binary (with the smallest, and only the smallest, of the two padded with the appropriate number of leading 0's so that both representations are the same number of binary digits long). OR respective binary digits. Here, each pair of respective digits OR'ed should be 1.
LINKS
MAPLE
Contribution from R. J. Mathar, Oct 09 2010: (Start)
isA000079 := proc(n) if type(n, 'even') then nops(numtheory[factorset](n)) = 1 ; else false ; fi ; end proc: read("transforms") ;
A175343 := proc(n) option remember; if n = 1 then 1; else for a from 1 do earl := false; for j from 1 to n-1 do if procname(j) = a then earl := true; break; end if; od ; if not earl then if isA000079(ORnos(a, procname(n-1))+1 ) then return a; end if; end if; end do: end if; end proc:
seq(A175343(n), n=1..80) ; (End)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Apr 17 2010
EXTENSIONS
More terms from R. J. Mathar, Oct 09 2010
STATUS
approved