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a(n) = smallest palindrome > a(n-1) such that a(1)*a(2)*...*a(n) + 1 and a(1)*a(2)*...*a(n) - 1 are primes.
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%I #17 Oct 14 2021 18:12:22

%S 4,363,434,484,494,636,4004,46864,47474,135531,695596,1793971,1826281,

%T 1933391,4700074,4785874,4806084,6462646,6574756,9558559,15399351,

%U 46288264,53500535,57499475,150787051,185808581,197636791,226686622

%N a(n) = smallest palindrome > a(n-1) such that a(1)*a(2)*...*a(n) + 1 and a(1)*a(2)*...*a(n) - 1 are primes.

%t a[1] = 4; a[n_] := a[n] = For[k = a[n-1]+1, True, k++, id = IntegerDigits[k]; If[id == Reverse[id], p = Product[a[j], {j, 1, n - 1}]*k + 1; If[PrimeQ[p] && PrimeQ[p-2], Return[k]]]]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 28}] (* _Jean-François Alcover_, Jul 30 2017 *)

%Y Cf. A051896, A051954.

%Y Subsequence of A002113.

%K nice,nonn,base

%O 1,1

%A _Felice Russo_, Dec 21 1999

%E a(12)-a(28) from _Donovan Johnson_, Feb 17 2010