%I A101274
%S A101274 1,2,4,5,8,10,14,21,15,16,26,25,34,22,48,38,71,40,74,90,28,69,113,47,94,
%T A101274 54,46,143,153,83,128,49,249,75,133,225,125,131,270,145,230
%N A101274 a(1)=1; for n>1, a(n) is the smallest positive integer such that the 
               set of all sums of adjacent elements up to and including a(n) contains 
               no number more than once.
%C A101274 Does the sequence together with the sums of adjacent elements include 
               all positive integers? Choosing starting values other than a(1)=1 
               gives other sequences. We could ask, for a given n, which such sequences 
               have the smallest sum of a(k) from k=1 to n.
%e A101274 a(8)=21 because the set of sums of adjacent elements to this point, call 
               it s(7) is {1,2,3,4,5,6,7,8,9,10,11,12,13,14,17,18,19,20,23,24,27,
               29,30,32,37,41,43,44}.
%e A101274 The first number missing from this list is 15, but a(8) cannot equal 
               15 because 15+14=29 and 29 is already in s(7). Similarly a(8) cannot 
               be 16 because 16+14=30.
%Y A101274 Sequence in context: A067941 A092265 A163295 this_sequence A080222 A050539 
               A039895
%Y A101274 Adjacent sequences: A101271 A101272 A101273 this_sequence A101275 A101276 
               A101277
%K A101274 nonn
%O A101274 1,2
%A A101274 David S Newman (DavidSNewman(AT)hotmail.com), Dec 20 2004