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A330434 a(1) = 1, a(2) = 2; thereafter a(n) = smallest number not occurring earlier such that the sum of three successive digits is prime.

%I A330434 #15 Jan 06 2020 21:26:52
%S A330434 1,2,4,5,8,6,3,20,9,22,7,24,10,11,13,17,31,15,51,19,35,33,53,37,39,55,
%T A330434 71,57,73,77,91,75,59,95,93,79,110,12,21,28,14,25,42,18,23,26,32,27,
%U A330434 40,16,41,60,50,29,62,30,43,44,34,45,48,54,49,46,38,63,80,52,47,64,36,83,68,56,61,66,58,65,84,70,67,401
%N A330434 a(1) = 1, a(2) = 2; thereafter a(n) = smallest number not occurring earlier such that the sum of three successive digits is prime.
%H A330434 Carole Dubois, <a href="/A330434/b330434.txt">Table of n, a(n) for n = 1..508</a>
%e A330434 After 8 and 6 the next term is 3 as 8+6+3 = 17 is a prime;
%e A330434 After 6 and 3 the next term is 20 as 6+3+2 = 11 and 3+2+0 = 5 are primes;
%e A330434 After 20 the next term is 9 as 2+0+9 = 11 is a prime; etc.
%t A330434 Nest[Append[#, Block[{k = 3}, While[Nand[FreeQ[#, k], AllTrue[Table[Total@ #[[i ;; i + 2]], {i, Length@ # - 2}], PrimeQ] &@ Flatten@ IntegerDigits@ Append[#, k] ], k++]; k]] &, {1, 2}, 80] (* _Michael De Vlieger_, Dec 14 2019 *)
%Y A330434 Cf. A076990 (3 successive terms have a prime sum), A330424 (3 successive terms AND 3 successive digits have a prime sum).
%K A330434 base,nonn
%O A330434 1,2
%A A330434 _Eric Angelini_ and _Carole Dubois_, Dec 14 2019