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A134736 a(1) = 5; for n >1, a(n) = a(n-1) + gcd(n, a(n-1)).

%I A134736 #15 Jan 25 2022 12:24:14
%S A134736 5,6,9,10,15,18,19,20,21,22,33,36,37,38,39,40,41,42,43,44,45,46,69,72,
%T A134736 73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,
%U A134736 141,144,145,150,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168
%N A134736 a(1) = 5; for n >1, a(n) = a(n-1) + gcd(n, a(n-1)).
%D A134736 Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc., 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986).
%H A134736 T. D. Noe, <a href="/A134736/b134736.txt">Table of n, a(n) for n=1..1000</a>
%H A134736 Eric S. Rowland, <a href="https://arxiv.org/abs/0710.3217">A natural prime-generating recurrence</a>, arXiv:0710.3217 [math.NT], 2007-2008.
%t A134736 a[1] = 5; a[n_] := a[n] = a[n-1] + GCD[n, a[n-1]];
%t A134736 Array[a, 66] (* _Jean-François Alcover_, Oct 01 2018 *)
%t A134736 RecurrenceTable[{a[1]==5,a[n]==a[n-1]+GCD[n,a[n-1]]},a,{n,70}] (* _Harvey P. Dale_, Nov 24 2018 *)
%o A134736 (Haskell)
%o A134736 a134736 n = a134736_list !! (n-1)
%o A134736 a134736_list =
%o A134736    5 : zipWith (+) a134736_list (zipWith gcd a134736_list [2..])
%o A134736 -- _Reinhard Zumkeller_, Nov 15 2013
%Y A134736 See A106108 for other cross-references.
%Y A134736 Cf. A230504, A134743 (first differences), A084662, A084663.
%K A134736 nonn
%O A134736 1,1
%A A134736 _N. J. A. Sloane_, Jan 28 2008