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%I #15 Aug 18 2024 02:01:13
%S 2,3,4,5,9,10,13,15,16,17,19,20,22,23,25,26,27,29,31,33,34,35,37,38,
%T 39,41,43,45,46,47,49,50,51,53,56,57,59,60,61,63,64,65,67,68,69,71,72,
%U 73,75,76,79,81,83,85,86,88,89,95,96,97,101,102,103,107,108,109,113,114
%N a(1) = 2; for n > 1, a(n) is smallest number, greater than a(n-1), which is relatively prime to the sum of all previous terms.
%e After 5 the next term is 9 as 2 + 3 + 4 + 5 = 14 and 6, 7 and 8 have common divisors with 14.
%p a[1]:=2: for m from 2 to 80 do b:=proc(n) if gcd(sum(a[j],j=1..m-1),n)=1 then n else fi end: M:=[seq(b(n),n=a[m-1]+1..200)]: a[m]:=M[1] od:seq(a[n],n=1..80); # _Emeric Deutsch_, Jul 18 2005
%o (PARI) first(n) = my(v = vector(n), s, t); s = v[1] = 2; for(i = 2, n, t=v[i-1]+1; while(gcd(t, s)!=1, t++); v[i]=t; s+=v[i]); v \\ _David A. Corneth_, Aug 11 2017
%K nonn,easy
%O 1,1
%A _Amarnath Murthy_, Jun 19 2001
%E Corrected and extended by _Emeric Deutsch_, Jul 18 2005