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a(n) = smallest palindrome > a(n-1) such that a(1)*a(2)*...*a(n) - 1 is a prime.
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%I #17 Oct 14 2021 15:58:28

%S 3,4,5,6,8,9,11,22,88,232,272,303,333,383,434,454,555,787,797,848,999,

%T 1331,3663,6666,10201,14041,15951,17271,21912,22122,24442,26662,33433,

%U 35053,40504,40804,44344,44644,44844,45754,55955,67976,72227,72627

%N a(n) = smallest palindrome > a(n-1) such that a(1)*a(2)*...*a(n) - 1 is a prime.

%H Harvey P. Dale, <a href="/A051954/b051954.txt">Table of n, a(n) for n = 1..100</a>

%t nxt[{p_,a_}]:=Module[{k=a+1},While[!PalindromeQ[k]||!PrimeQ[p*k-1],k++];{p*k,k}]; NestList[nxt,{3,3},50][[All,2]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 22 2021 *)

%Y Cf. A051896, A051934.

%Y Subsequence of A002113.

%K nice,nonn,base

%O 1,1

%A _Felice Russo_, Dec 21 1999