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A051934 a(n) is the smallest palindrome > a(n-1) such that a(1)+a(2)+...+a(n) is a prime.

%I A051934 #29 Jul 08 2024 16:28:31
%S A051934 2,3,6,8,22,66,242,252,262,414,444,626,676,686,808,2442,2552,2992,
%T A051934 4664,4884,6006,6226,6666,8228,20202,20302,20402,40204,40304,60606,
%U A051934 61116,61716,80608,202202,207702,212212,402204,405504,609906,619916,623326,801108
%N A051934 a(n) is the smallest palindrome > a(n-1) such that a(1)+a(2)+...+a(n) is a prime.
%C A051934 a(n) is even except for n = 2. - _Chai Wah Wu_, Aug 30 2021
%H A051934 Chai Wah Wu, <a href="/A051934/b051934.txt">Table of n, a(n) for n = 1..186</a> (terms 1..100 from Reinhard Zumkeller)
%t A051934 palQ[n_] := Reverse[x = IntegerDigits[n]] == x; t = {s = 2}; Do[If[palQ[n] && PrimeQ[x = s + n], AppendTo[t, n]; s = x], {n, 3, 815000}]; t (* _Jayanta Basu_, Jun 24 2013 *)
%t A051934 sp[{t_,a_}]:=Module[{k=a+1},While[!PalindromeQ[k]||!PrimeQ[t+k],k++];{t+k,k}]; NestList[ sp,{2,2},50][[;;,2]] (* _Harvey P. Dale_, Jul 08 2024 *)
%o A051934 (Haskell)
%o A051934 a051934 n = a051934_list !! (n-1)
%o A051934 a051934_list = f 0 a002113_list where
%o A051934    f x (m:ms) | a010051 (x + m) == 1 = m : f (x + m) ms
%o A051934               | otherwise            = f x ms
%o A051934 -- _Reinhard Zumkeller_, Dec 28 2011
%Y A051934 Cf. A002113, A010051, A051896, A087581.
%K A051934 easy,nice,nonn,base
%O A051934 1,1
%A A051934 _Felice Russo_, Dec 21 1999
%E A051934 Missing a(29)=40304 inserted by _Reinhard Zumkeller_, Dec 28 2011