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A199162 a(1) = 1, a(2) = 6; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms.

%I A199162 #9 Feb 16 2025 08:33:16
%S A199162 1,6,7,8,9,10,11,12,14,24,26,27,28,29,31,45,46,47,48,49,62,68,82,83,
%T A199162 84,85,98,104,117,122,135,142,154,155,159,172,191,192,193,194,195,209,
%U A199162 234,245,248,249,250,265,266,267,268,270,283,302,303,304,305,306
%N A199162 a(1) = 1, a(2) = 6; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms.
%C A199162 An Ulam-type sequence - see A002858 for many further references, comments, etc.
%H A199162 Reinhard Zumkeller, <a href="/A199162/b199162.txt">Table of n, a(n) for n = 1..10000</a>
%H A199162 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>
%H A199162 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>
%H A199162 <a href="/index/U#Ulam_num">Index entries for Ulam numbers</a>
%e A199162 13 is not a term, as 13 = 7+6 = a(3)+a(2) and 13 = 12+1 = a(8)+a(1);
%e A199162 14 is a term, because 14 = 8 + 6 = a(4) + a(2) is unique for distinct terms, a(9) = 14.
%o A199162 (Haskell)
%o A199162 a199162 n = a199162_list !! (n-1)
%o A199162 a199162_list = 1 : 6 : ulam 2 6 a199162_list
%o A199162 -- Function ulam as defined in A002858.
%o A199162 -- _Reinhard Zumkeller_, Nov 03 2011
%Y A199162 Cf. A003663.
%K A199162 nonn
%O A199162 1,2
%A A199162 _Reinhard Zumkeller_, Nov 03 2011