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a(0) = 3; for n > 0, a(n) is the greatest prime factor of PreviousPrime(a(n-1))*a(n-1)-1 where PreviousPrime(prime(k))=prime(k-1).
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%I #14 Apr 19 2016 01:07:31

%S 3,5,7,17,11,19,23,109,17,11,19,23,109,17,11,19,23,109,17,11,19,23,

%T 109,17,11,19,23,109,17,11,19,23,109,17,11,19,23,109,17,11,19,23,109,

%U 17,11,19,23,109,17,11,19,23,109,17,11,19,23,109,17,11,19,23,109,17,11,19,23

%N a(0) = 3; for n > 0, a(n) is the greatest prime factor of PreviousPrime(a(n-1))*a(n-1)-1 where PreviousPrime(prime(k))=prime(k-1).

%H Harvey P. Dale, <a href="/A031441/b031441.txt">Table of n, a(n) for n = 0..1000</a>

%e To get a(3) we compute PreviousPrime(7)=5, 5*7-1=34, greatest prime factor of 34 is 17, so a(3)=17.

%t a[0] = 3; a[n_] := a[n] = FactorInteger[ NextPrime[ a[n-1], -1]*a[n-1] - 1][[-1, 1]]; Table[a[n], {n, 0, 66}] (* _Jean-François Alcover_, Mar 09 2012 *)

%t NestList[FactorInteger[NextPrime[#,-1]*#-1][[-1,1]]&,3,70] (* _Harvey P. Dale_, Dec 13 2012 *)

%Y Cf. A034970, A031442.

%K nonn,easy,nice

%O 0,1

%A _Yasutoshi Kohmoto_

%E More terms from _James A. Sellers_