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A055498 a(0)=0, a(1)=1, a(n) = smallest prime >= a(n-1) + a(n-2).

%I A055498 #39 Jan 20 2025 10:59:37
%S A055498 0,1,2,3,5,11,17,29,47,79,127,211,347,563,911,1481,2393,3877,6271,
%T A055498 10151,16427,26591,43019,69623,112643,182279,294923,477209,772139,
%U A055498 1249361,2021501,3270863,5292367,8563237,13855607,22418849,36274471,58693331,94967809,153661163
%N A055498 a(0)=0, a(1)=1, a(n) = smallest prime >= a(n-1) + a(n-2).
%H A055498 Zak Seidov and Robert G. Wilson v, <a href="/A055498/b055498.txt">Table of n, a(n) for n = 0..1001</a> (first 101 terms from Zak Seidov)
%F A055498 a(n+1) = nextprime(a(n) + a(n-1)) where nextprime(n) is smallest prime >= n.
%F A055498 a(n) is asymptotic to c*phi^n where phi = (1 + sqrt(5))/2 and c = 1.086541275044988562375... - _Benoit Cloitre_, May 02 2004
%F A055498 a(n) = A055499(n-1) for n>3. - _Robert G. Wilson v_, Mar 13 2013
%F A055498 a(n) = A007918(a(n-1) + a(n-2)) for n > 1. - _Reinhard Zumkeller_, Nov 13 2014
%e A055498 After 3, 5, the next prime >=8 is 11.
%t A055498 a[0] = 0; a[1] = 1; a[n_] := a[n] = NextPrime[a[n - 1] + a[n - 2] -1]; Array[a, 37, 0] (* _Robert G. Wilson v_, Mar 13 2013 *)
%t A055498 RecurrenceTable[{a[0]==0,a[1]==1,a[n]==NextPrime[a[n-1]+a[n-2]-1]},a,{n,50}] (* _Harvey P. Dale_, May 08 2013 *)
%o A055498 (PARI) a(n)=local(v);if(n<2,n>=0,n++;v=vector(n,i,1);for(i=3,n,v[i]=nextprime(v[i-1]+v[i-2]));v[n]) /* _Michael Somos_, Feb 01 2004 */
%o A055498 (Haskell)
%o A055498 a055498 n = a055498_list !! n
%o A055498 a055498_list = 0 : 1 : map a007918
%o A055498     (zipWith (+) a055498_list $ tail a055498_list)
%o A055498 -- _Reinhard Zumkeller_, Nov 13 2014
%Y A055498 Cf. A073021, A073022, A055499, A055500, A055501, A055502.
%Y A055498 Cf. A007918.
%K A055498 nonn
%O A055498 0,3
%A A055498 _N. J. A. Sloane_, Jul 08 2000