%I #29 Oct 12 2018 21:59:02

%S 3,5,6,9,10,11,13,17,18,19,20,22,23,25,28,33,34,35,36,37,39,40,41,43,

%T 44,46,49,50,52,55,59,65,66,67,68,69,70,72,73,74,75,77,78,79,81,82,84,

%U 87,88,89,91,92,94,97,98,100,103,107,108,110,113,117,122,129,130,131,132

%N Numbers which occur only once in A004001.

%C Out of the first one million terms (a(10^6) = 510403), 258661 occur only once.

%C Complement of A087686; A051135(a(n)) = 1. - _Reinhard Zumkeller_, Jun 03 2011

%C From _Antti Karttunen_, Jan 18 2016: (Start)

%C In general, out of the first 2^(n+1) terms of A004001, 2^(n-1) - 1 terms (a quarter) occur only once. See also illustration in A265332.

%C One more than the positions of ones in A093879.

%C (End)

%H Reinhard Zumkeller, <a href="/A088359/b088359.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Antti Karttunen_, Jan 18 2016: (Start)

%F Other identities.

%F For all n >= 0, a(A000079(n)) = A000051(n+1), that is, a(2^n) = 2^(n+1) + 1.

%F For all n >= 1:

%F a(n) = A004001(A266399(n)).

%F (End)

%t a[1] = 1; a[2] = 1; a[n_] := a[n] = a[ a[n - 1]] + a[n - a[n - 1]]; hc = Table[ a[n], {n, 1, 261}]; RunLengthEncodeOne[x_List] := Length[ # ] == 1 & /@ Split[x]; r = RunLengthEncodeOne[hc]; Select[ Range[ Length[r]], r[[ # ]] == True &]

%o (Haskell)

%o import Data.List (elemIndices)

%o a088359 n = a088359_list !! (n-1)

%o a088359_list = map succ $ elemIndices 1 a051135_list

%o -- _Reinhard Zumkeller_, Jun 03 2011

%o (Scheme, with Antti Karttunen's IntSeq-library)

%o (define A088359 (ZERO-POS 1 1 (COMPOSE -1+ A051135)))

%o ;; _Antti Karttunen_, Jan 18 2016

%Y Positions of ones in A051135.

%Y Cf. A188163 (same sequence with prepended 1).

%Y Cf. A087686 (complement).

%Y Cf. A004001, A093879, A265332, A266399.

%Y Cf. also A267110, A267111, A267112.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Sep 26 2003