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%I
%S 7,8,9,10,15,18,19,20,21,22,33,36,37,38,39,40,41,42,43,44,45,46,69,72,
%T 73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,
%U 141,144,145,150,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168
%N Rowland's prime-generating sequence: a(1) = 7; for n >1, a(n) = a(n-1) + gcd(n, a(n-1)).
%C The title refers to the sequence of first differences, A132199.
%C Setting a(1) = 4 gives A084662.
%C Rowland proves that the first differences are all 1's or primes. The prime differences form A137613.
%C See A137613 for additional comments, links and references. [From _Jonathan Sondow_, Aug 14 2008]
%C "This recurrence was discovered at the 2003 NKS Summer School by a group led by Matt Frank. This Demonstration allows initial conditions . a(1) >= 4. For 1 =< a(1) =< 3, a(n) - a(n-1) is 1 for n >= 3." See Wolfram hyperlink. [From _Robert G. Wilson v_, Sep 10 2008]
%D Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc., 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986).
%H T. D. Noe, <a href="/A106108/b106108.txt">Table of n, a(n) for n=1..1000</a>
%H Fernando Chamizo, Dulcinea Raboso and Serafin Ruiz-Cabello, <a href="http://www.combinatorics.org/Volume_18/Abstracts/v18i2p10.html">On Rowland's sequence</a>, Electronic J. Combin., Vol. 18(2), 2011, #P10.
%H Eric S. Rowland, <a href="http://arXiv.org/abs/0710.3217">A simple prime-generating recurrence</a>.
%H Eric S. Rowland, <a href="http://demonstrations.wolfram.com/PrimeGeneratingRecurrence/"> Prime-Generating Recurrence</a>, Wolfram Demonstrations Project. [From _Robert G. Wilson v_, Sep 10 2008]
%p S:=7; f:= proc(n) option remember; global S; if n=1 then RETURN(S); else RETURN(f(n-1)+gcd(n,f(n-1))); fi; end; [seq(f(n),n=1..200)];
%t a[1] = 7; a[n_] := a[n] = a[n - 1] + GCD[n, a[n - 1]]; Array[a, 66] (* From _Robert G. Wilson v_, Sep 10 2008 *)
%o (PARI) a=vector(100);a[1]=7;for(n=2,#a,a[n]=a[n-1]+gcd(n,a[n-1]));a \\ _Charles R Greathouse IV_, Jul 15 2011
%Y Cf. A084662, A084663, A132199, A134734, A134736, A134743, A134744, A134162, A137613, A221869.
%K nonn,changed
%O 1,1
%A _N. J. A. Sloane_, Jan 28 2008
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