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.

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, 71, 57, 73, 77, 91, 75, 59, 95, 93, 79, 110, 12, 21, 28, 14, 25, 42, 18, 23, 26, 32, 27, 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

Offset: 1

Author

Eric Angelini and Carole Dubois, Dec 14 2019

Keywords

• base
• nonn

Examples

			After 8 and 6 the next term is 3 as 8+6+3 = 17 is a prime;
After 6 and 3 the next term is 20 as 6+3+2 = 11 and 3+2+0 = 5 are primes;
After 20 the next term is 9 as 2+0+9 = 11 is a prime; etc.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..508

Crossrefs

Cf. A076990 (3 successive terms have a prime sum), A330424 (3 successive terms AND 3 successive digits have a prime sum).

Programs

Mathematica

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 *)