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Take sequence A000005 (where A000005(n) = the number of divisors of n). To get {a(k)}, replace each run of multiple occurrences of the same integer in sequence A000005 with just one occurrence of that integer, such that a(n) never equals a(n+1).
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%I #9 Mar 04 2019 01:24:10

%S 1,2,3,2,4,2,4,3,4,2,6,2,4,5,2,6,2,6,4,2,8,3,4,6,2,8,2,6,4,9,2,4,8,2,

%T 8,2,6,4,2,10,3,6,4,6,2,8,4,8,4,2,12,2,4,6,7,4,8,2,6,4,8,2,12,2,4,6,4,

%U 8,2,10,5,4,2,12,4,8,2,12,4,6,4,12,2,6,9,2,8,2,8,4,2,12,2,8,4,10,2,8,4,6,4

%N Take sequence A000005 (where A000005(n) = the number of divisors of n). To get {a(k)}, replace each run of multiple occurrences of the same integer in sequence A000005 with just one occurrence of that integer, such that a(n) never equals a(n+1).

%p read("transforms3") ; a000005 := BFILETOLIST("b000005.txt") ; op(1..120,LISTNODUPL(a000005)) ; # _R. J. Mathar_, Aug 01 2009

%Y Cf. A000005.

%K nonn

%O 1,2

%A _Leroy Quet_, Jul 01 2009

%E More terms from _R. J. Mathar_, Aug 01 2009